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Coulomb branches of quiver gauge theories with symmetrizersJul 15 2019We generalize the mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ SUSY quiver gauge theories in arXiv:1503.03676, arXiv:1601.03686, arXiv:1604.03625 to the cases with symmetrizers. We obtain generalized affine Grassmannian ... More

Quantum $N$-toroidal algebras and extended quantized GIM algebras of $N$-fold affinizationJul 15 2019We give a general definition of quantum $N$-toroidal algebras uniformly, which is a natural generalization of classical quantum toroidal algebras, as well as extended quantized GIM algebras of $N$-fold affinization. We show that quantum $N$-toroidal algebras ... More

Quadratic Algebras arising from Hopf operads generated by a single elementJul 12 2019The operads of Poisson and Gerstenhaber algebras are generated by a single binary element if we consider them as Hopf operads (i.e. as operads in the category of cocommutative coalgebras). In this note we discuss in details the Hopf operads generated ... More

Degeneration of spectral sequences and complex Lagrangian submanifoldsJul 10 2019There is a local-to-global $\mathrm{Ext}$ spectral sequence $\mathrm{E}_2^{p,q} = \mathrm{H}^p(\mathrm{L}, \Omega^q_\mathrm{L}) \Rightarrow \mathrm{Ext}^{p+q}(i_*\mathscr{O}_\mathrm{L}, i_*\mathscr{O}_{\mathrm{L}})$ for a smooth Lagrangian subvariety ... More

Symmetry defects and orbifolds of two-dimensional Yang-Mills theoryJul 10 2019We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path ... More

Generalized symmetry in noncommutative complex geometryJul 10 2019We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop a general framework of noncommutative complex geometry that subsumes the one in \cite{MR3720811}. We present transverse complex and K\"ahler structures ... More

Supersymmetric Wilson Loops, Instantons, and Deformed W-AlgebrasJul 08 2019Let $\mathfrak{g}$ be a simple Lie algebra. We study half-BPS Wilson loops of supersymmetric 5d $\mathfrak{g}$-type quiver gauge theories on a circle, in a non-trivial instanton background. The Wilson loops are codimension 4 defects of the gauge theory, ... More

Separation of variables and scalar products at any rankJul 08 2019Separation of variables (SoV) is a special property of integrable models which ensures that the wavefunction has a very simple factorised form in a specially designed basis. Even though the factorisation of the wavefunction was recently established for ... More

The Euler characteristic of $\operatorname{Out}(F_n)$Jul 08 2019We prove that the rational Euler characteristic of $\operatorname{Out}(F_n)$ is always negative and its asymptotic growth rate is $\Gamma(n- \frac32)/\sqrt{2\pi} \log^2 n$. This settles a 1987 conjecture of J. Smillie and the second author. We establish ... More

The meromorphic R-matrix of the YangianJul 08 2019Let g be a complex semisimple Lie algebra and Yg the Yangian of g. The main goal of this paper is to clarify the analytic nature of Drinfeld's universal R-matrix of Yg. It is known that the radius of convergence of R(s) on the tensor product of two finite-dimensional ... More

Skew lattices and set-theoretic solutions of the Yang-Baxter equationJul 08 2019In this paper we discuss and characterize several set-theoretic solutions of the Yang-Baxter equation obtained using skew lattices, an algebraic structure that has not yet been related to the Yang-Baxter equation. Such solutions are degenerate in general, ... More

Strict quantization of coadjoint orbitsJul 06 2019We obtain a strict quantization of the holomorphic functions on any semisimple coadjoint orbit of a complex semisimple connected Lie group. By restricting this quantization, we also obtain strict star products on a subalgebra of analytic functions for ... More

Rigidity and derived isomorphism problem for enveloping algebrasJul 05 2019Jul 11 2019We prove that there are no injective homomorphisms between enveloping algebras of non-isomorphic semi-simple Lie algebras of the same dimension. We also describe the center of reduction modulo large prime $p$ of the enveloping algebra of an algebraic ... More

Rigidity and derived isomorphism problem for enveloping algebrasJul 05 2019We prove that there are no injective homomorphisms between enveloping algebras of non-isomorphic semi-simple Lie algebras of the same dimension. We also describe the center of reduction modulo large prime $p$ of the enveloping algebra of an algebraic ... More

Quantum Enhancements via Tribracket BracketsJul 05 2019We enhance the tribracket counting invariant with \textit{tribracket brackets}, skein invariants of tribracket-colored oriented knots and links analogously to biquandle brackets. This infinite family of invariants includes the classical quantum invariants ... More

Kazama-Suzuki coset construction and its inverseJul 04 2019We study the representation theory of the Kazama-Suzuki coset vertex operator superalgebra associated with the pair of a complex simple Lie algebra and its Cartan subalgebra. In the case of type $A_{1}$, B.L. Feigin, A.M. Semikhatov, and I.Yu. Tipunin ... More

Weak integral forms and the sixth Kaplansky conjectureJul 04 2019It is a short unpublished note from 1998. I make it public because Cuadra and Meir refer to it in their paper. We precisely state and prove a folklore result that if a finite dimensional semisimple Hopf algebra admits a weak integral form then it is of ... More

Duality for Bethe algebras acting on polynomials in anticommuting variablesJul 03 2019We consider actions of the current Lie algebras $\mathfrak{gl}_{n}[t]$ and $\mathfrak{gl}_{k}[t]$ on the space of polynomials in $kn$ anticommuting variables. The actions depend on parameters $\bar{z}=(z_{1}\dots z_{k})$ and $\bar{\alpha}=(\alpha_{1}\dots ... More

Formality morphism as the mechanism of $\star$-product associativity: how it worksJul 01 2019The formality morphism $\boldsymbol{\mathcal{F}}=\{\mathcal{F}_n$, $n\geqslant1\}$ in Kontsevich's deformation quantization is a collection of maps from tensor powers of the differential graded Lie algebra (dgLa) of multivector fields to the dgLa of polydifferential ... More

Mellin-Barnes presentations for Whittaker wave functionsJul 01 2019We obtain certain Mellin-Barnes integrals which present Whittaker wave functions related to classical real split forms of simple complex Lie groups.

Fusion products of twisted modules in permutation orbifoldsJun 28 2019Let $V$ be a vertex operator algebra, $k$ a positive integer and $\sigma$ a permutation automorphism of the vertex operator algebra $V^{\otimes k}$. In this paper, we determine the fusion product of any $V^{\otimes k}$-module with any $\sigma$-twisted ... More

Lectures on Factorization Homology, Infinity-Categories, and Topological Field TheoriesJun 28 2019These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.

Theta functions and quiver GrassmanniansJun 28 2019In this article, we use the relationship between cluster scattering diagrams and stability scattering diagrams to relate quiver representations with these diagrams. With a notion of positive crossing of a path $\gamma$, we show that if $\gamma$ has positive ... More

Quantum periodicity and Kirillov-Reshetikhin modulesJun 28 2019We give a proof of the periodicity of quantum $T$-systems of type $A_n\times A_\ell$ with certain spiral boundary conditions. Our proof is based on categorification of the $T$-system in terms of the representation theory of quantum affine algebras, more ... More

Quantum generalized Kac--Moody algebras via Hall algebras of complexesJun 28 2019We establish an embedding of the quantum enveloping algebra of a symmetric generalized Kac--Moody algebra into a localized Hall algebra of $\mathbb Z_2$-graded complexes of representations of a quiver with (possible) loops. To overcome difficulties resulting ... More

Existence of quantum symmetries for graphs on up to seven vertices: a computer based approachJun 28 2019The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In general, there ... More

Irregular vertex algebrasJun 28 2019We introduce the notion of irregular vertex (operator) algebras. The irregular versions of fundamental properties, such as Goddard uniqueness theorem, associativity and operator product expansions are formulated and proved. We also give some elementary ... More

Comparison of spaces associated to DGLA via higher holonomyJun 27 2019Fof a nilpotent differential graded Lie algebra whose components vanish in degrees below -1 we construct an explicit equivalence between the nerve of the Deligne 2-groupoid and the simplicial set of differential forms with values in the Lie algebra introduced ... More

Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VI. Suzuki and Ree groupsJun 27 2019We analyse the rack structure of conjugacy classes in simple Suzuki and Ree groups and determine which classes are kthulhu. Combining this results with abelian rack techniques, we show that the only finite-dimensional complex pointed Hopf algebras over ... More

2-representations of Soergel bimodulesJun 27 2019In this paper we study the graded 2-representation theory of Soergel bimodules for a finite Coxeter group. We establish a precise connection between the graded 2-representation theory of this non-semisimple 2-category and the 2-representation theory of ... More

Burnside rings for Real $2$-representation theory: The linear theoryJun 26 2019Jul 02 2019This paper is a fundamental study of the Real $2$-representation theory of $2$-groups. It also contains many new results in the ordinary (non-Real) case. Our framework relies on a $2$-equivariant Morita bicategory, where a novel construction of induction ... More

Burnside rings for Real $2$-representation theory: The linear theoryJun 26 2019This paper is a fundamental study of the Real $2$-representation theory of $2$-groups. It also contains many new results in the usual (non-Real) case. Our framework relies on a $2$-equivariant Morita bicategory, where a novel construction of induction ... More

Higher depth quantum modular forms and plumbed $3$-manifoldsJun 25 2019In this paper we study new invariants $\widehat{Z}_{\boldsymbol{a}}(q)$ attached to plumbed $3$-manifolds that were introduced by Gukov, Pei, Putrov, and Vafa. These remarkable $q$-series at radial limits conjecturally compute WRT invariants of the corresponding ... More

Quantization of Poisson Hopf algebrasJun 25 2019We describe a method for quantization of Poisson Hopf algebras in $\mathbb Q$-linear symmetric monoidal categories. It is compatible with tensor products and can also be used to produce braided Hopf algebras. The main idea comes from the fact that nerves ... More

Models of quantum permutationsJun 25 2019For $N\ge 4$ we present a series of *-homomorphisms $\varphi_n:C(S_N^+)\rightarrow B_n$ where $S_N^+$ is the quantum permutation group. They are not necessarily representations of the quantum group $S_N^+$ but they yield good operator algebraic models ... More

Pentad and triangular structures behind the Racah matricesJun 24 2019Somewhat unexpectedly, the study of the family of twisted knots revealed a hidden structure behind exclusive Racah matrices $\bar S$, which control non-associativity of the representation product in a peculiar channel $R\otimes \bar R \otimes R \longrightarrow ... More

On the uniqueness of invariant statesJun 24 2019Given an abelian group G endowed with a T-pre-symplectic form, we assign to it a symplectic twisted group *-algebra W_G and then we provide criteria for the uniqueness of states invariant under the ergodic action of the symplectic group of automorphism. ... More

On the uniqueness of unitary structure for unitarizable fusion categoriesJun 24 2019We prove that every unitarizable fusion category admits a unique unitary structure. More generally, we show that the forgetful 2-functor from the 2-groupoid of unitary fusion categories, unitary monoidal equivalences and unitary monoidal natural isomorphisms ... More

Random Finite Noncommutative Geometries and Topological RecursionJun 22 2019In this paper we investigate a model for quantum gravity on finite noncommutative spaces using the theory of blobbed topological recursion. The model is based on a particular class of random finite real spectral triples ${(\mathcal{A}, \mathcal{H}, D ... More

On quantum $K$-groups of partial flag manifoldsJun 21 2019We show that the equivariant small quantum $K$-group of a partial flag manifold is a quotient of that of the full flag manifold as a based ring. This yields a variant of the $K$-theoretic analogue of the parabolic version of Peterson's theorem [Lam-Shimozono, ... More

Simplicity of spectra for Bethe subalgebras in $Y(\mathfrak{gl}_2)$Jun 21 2019We consider Bethe subalgebras B(C) in the Yangian $Y(\mathfrak{gl}_2)$ with $C$ regular $2\times 2$ matrix. We study the action of Bethe subalgebras of $Y(\mathfrak{gl}_2)$ on finite-dimensional representations of $Y(\mathfrak{gl}_2)$. We prove that $B(C)$ ... More

Braid group representations from twisted tensor products of algebrasJun 19 2019We unify and generalize several approaches to constructing braid group representations from finite groups, using iterated twisted tensor products. Our results hint at a relationship between the braidings on the $G$-gaugings of a pointed modular category ... More

The Fulton Mac Pherson operad and the W-constructionJun 18 2019In this short note we explain in detail the construction of a $O(n)$-equivariant isomorphism of topological operads $F_n \cong WF_n$ , where $F_n$ is the Fulton Mac Pherson operad and $W$ is the Boardman-Vogt construction

A cell decomposition of the Fulton MacPherson operadJun 18 2019We construct a regular cellular decomposition of the Fulton MacPherson operad $FM_2$ that is compatible with the operad composition. The cells are indexed by trees with edges of two colors and vertices labelled by cells of the cacti operad. This answers ... More

Infinite families of potential modular data related to quadratic categoriesJun 18 2019We present several infinite families of potential modular data motivated by examples of Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric groups with Gauss sums differing by a sign, along with some conditions ... More

Quantum determinant revisitedJun 17 2019Following [G] we define quantum determinants in certain quantum algebras, related to couples of compatible braidings. Also, we compare these quantum determinants with the highest elementary symmetric polynomials. Some properties of the quantum determinants ... More

Braided Tensor Categories related to $\mathcal{B}_p$ Vertex AlgebrasJun 17 2019The $\mathcal{B}_p$-algebras are a family of vertex operator algebras parameterized by $p\in \mathbb Z_{\geq 2}$. They are important examples of logarithmic CFTs and appear as chiral algebras of type $(A_1, A_{2p-3})$ Argyres-Douglas theories. The first ... More

On non-connected pointed Hopf algebras of dimension 16 in characteristic 2Jun 16 2019Let $\mathds{k}$ be an algebraically closed field. We give a complete isomorphism classification of non-connected pointed Hopf algebras of dimension $16$ with $\operatorname{char}\mathds{k}=2$ that are generated by group-like elements and skew-primitive ... More

A homotopy Lie formula for the p-adic Dwork Frobenius operatorJun 15 2019We give a modern deformation theoretic interpretation of Dwork's theory of the zeta function of a smooth projective complete intersection variety $X$ over a finite field. Using this interpretation, we explicitly construct a dgla (differential graded Lie ... More

On the quantum symmetry of distance-transitive graphsJun 15 2019In this article, we study quantum automorphism groups of distance-transitive graphs. We show that the odd graphs, the Hamming graphs $H(n,3)$, the Johnson graphs $J(n,2)$ and the Kneser graphs $K(n,2)$ do not have quantum symmetry. We also give a table ... More

Braided dendriform and tridendriform algebras and braided Hopf algebras of planar treesJun 15 2019This paper introduces the braidings of dendriform algebras and tridendriform algebras. By studying free braided dendriform algebras, we obtain braidings of the Hopf algebras of Loday and Ronco of planar binary rooted trees. We also give a variation of ... More

Peter-Weyl bases, preferred deformations, and Schur-Weyl dualityJun 14 2019We discuss the deformed function algebra of a simply connected reductive Lie group G over the complex numbers using a basis consisting of matrix elements of finite dimensional representations. This leads to a preferred deformation, meaning one where the ... More

Total positivity is a quantum phenomenon: the grassmannian caseJun 14 2019The main aim of this paper is to establish a deep link between the totally nonnegative grassmannian and the quantum grassmannian. More precisely, under the assumption that the deformation parameter $q$ is transcendental, we show that "quantum positroids" ... More

Perturbative analysis of the colored Alexander polynomial and KP soliton $τ$-functionsJun 13 2019In this paper we elaborate on the statement given in arXiv:1805.02761. Mainly, we study the relation between the colored Alexander polynomial and the famous KP hierarchy. We explain and prove this relation by exploring the fact that the dispersion equations ... More

Logarithmic modules for chiral differential operators of nilmanifoldsJun 13 2019We describe explicitly the vertex algebra of (twisted) chiral differential operators on certain nilmanifolds and construct their logarithmic modules. This is achieved by generalizing the construction of vertex operators in terms of exponentiated scalar ... More

Two-cocycles and cleft extensions in left braided categoriesJun 12 2019We define two-cocycles and cleft extensions in categories that are not necessarily braided, but where specific objects braid from one direction, like for a Hopf algebra $H$ a Yetter-Drinfeld module braids from the left with $H$-modules. We will generalize ... More

On the structure of quantum vertex algebrasJun 12 2019A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998. In a nutshell, a quantum vertex algebra is a braided state-field correspondence which satisfies associativity and braided ... More

Twisted characters and holomorphic symmetriesJun 10 2019We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the twist explicitly ... More

Colored Vertex Models and Iwahori Whittaker FunctionsJun 10 2019We give a recursive method for computing all values of a basis of Iwahori Whittaker functions on a split reductive group $G$ over a nonarchimedean local field $F$ using an action of the Hecke algebra. Then we specialize to $G=GL_r$ where we show that ... More

Colored Vertex Models and Iwahori Whittaker FunctionsJun 10 2019Jul 12 2019We give a recursive method for computing all values of a basis of Iwahori Whittaker functions on a split reductive group $G$ over a nonarchimedean local field $F$ using an action of the Hecke algebra. Then we specialize to $G=GL_r$ where we show that ... More

The Quantum Flag Manifold $\mathbf{SU_q(3)/\mathbb{T}^2}$ as an Example of a Noncommutative Sphere BundleJun 10 2019Jun 11 2019The quantum flag manifold ${SU_q(3)/\mathbb{T}^2}$ is interpreted as a noncommutative bundle over the quantum complex projective plane with the quantum or Podle\'s sphere as a fibre. A connection arising from the (associated) quantum principal $U_q(2)$-bundle ... More

A topological model for the coloured Alexander invariantsJun 10 2019Coloured Alexander polynomials form a sequence of non-semisimple quantum invariants coming from the representation theory of the quantum group $U_q(sl(2))$ at roots of unity. This sequence recovers the original Alexander polynomial as the first term. ... More

Multipermutation distributive solutions of Yang-Baxter equation have nilpotent permutation groupsJun 10 2019We investigate a class of non-involutive solutions of the Yang-Baxter equation which generalize self-distributive (derived) solutions. In particular, we study generalized multipermutation solutions in this class. We show that the Yang-Baxter (permutation) ... More

Noncommutative minimal embeddings and morphisms of pseudo-Riemannian calculiJun 10 2019In analogy with classical submanifold theory, we introduce morphisms of real metric calculi together with noncommutative embeddings. We show that basic concepts, such as the second fundamental form and the Weingarten map, translate into the noncommutative ... More

Homotopy transfer and formalityJun 08 2019In a recent paper, the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, $n$-formality of a differential graded algebraic structure is equivalent to the existence of a chain-level lift of a homology-level degree ... More

Finite dimensional irreducible representations of the nullity 2 centreless core $\mathfrak{g}_{2n,ρ}(\mathbb{C}_q)$Jun 08 2019We study the finite-dimensional irreducible representations of the nullity 2 centreless core $\mathfrak{g}_{2n,\rho}(\mathbb{C}_q)$ by investigating the structure of the $\mathrm{BC}_n$-graded Lie algebra $\mathfrak{g}_{2n,\rho}(R)$, where $R$ is a unital ... More

Antipodes, preantipodes and Frobenius functorsJun 08 2019We prove that a quasi-bialgebra admits a preantipode if and only if the associated free quasi-Hopf bimodule functor is Frobenius, if and only if the relative (opmonoidal) monad is a Hopf monad. The same results hold in particular for a bialgebra, tightening ... More

Relaxed highest-weight modules II: classifications for affine vertex algebrasJun 07 2019Jul 02 2019This is the second of a series of articles devoted to the study of relaxed highest-weight modules over affine vertex algebras and W-algebras. The first studied the simple "rank-$1$" affine vertex superalgebras $L_k(\mathfrak{sl}_2)$ and $L_k(\mathfrak{osp}(1\vert2))$, ... More

Relaxed highest-weight modules II: classifications for affine vertex algebrasJun 07 2019This is the second of a series of articles devoted to the study of relaxed highest-weight modules over affine vertex algebras and W-algebras. The first studied the simple "rank-$1$" affine vertex superalgebras $L_k(\mathfrak{sl}_2)$ and $L_k(\mathfrak{osp}(1\vert2))$, ... More

Tensor algebras in finite tensor categoriesJun 06 2019Jun 28 2019This paper introduces methods for classifying actions of finite-dimensional Hopf algebras on path algebras of quivers, and more generally on tensor algebras $T_B(V)$ where $B$ is a semisimple $\Bbbk$-algebra and $V$ is a $B$-bimodule. We do this by working ... More

Tensor algebras in finite tensor categoriesJun 06 2019This paper introduces methods for classifying actions of finite-dimensional Hopf algebras on path algebras of quivers, and more generally on tensor algebras $T_B(V)$ where $B$ is a semisimple $\Bbbk$-algebra and $V$ is a $B$-bimodule. We do this by working ... More

The Plancherel formula for complex semisimple quantum groupsJun 06 2019We calculate the Plancherel formula for complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups. As a consequence we obtain a concrete description of their associated reduced group $ C^* $-algebras. ... More

Localization of 4d $\mathcal{N}=1$ theories on $\mathbb{D}^2\times \mathbb{T}^2$Jun 05 2019We consider 4d $\mathcal{N}=1$ gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results ... More

Quantization of subgroups of the affine groupJun 05 2019Consider a locally compact group $G=Q\ltimes V$ such that $V$ is abelian and the action of $Q$ on the dual abelian group $\hat V$ has a free orbit of full measure. We show that such a group $G$ can be quantized in three equivalent ways: (1) by reflecting ... More

Quantization of subgroups of the affine groupJun 05 2019Jun 26 2019Consider a locally compact group $G=Q\ltimes V$ such that $V$ is abelian and the action of $Q$ on the dual abelian group $\hat V$ has a free orbit of full measure. We show that such a group $G$ can be quantized in three equivalent ways: (1) by reflecting ... More

Finite-dimensional irreducible modules of the universal Askey--Wilson algebra at roots of unityJun 05 2019Let $\mathbb F$ denote an algebraically closed field and assume that $q\in \mathbb F$ is a primitive $d^{\rm \, th}$ root of unity with $d\not=1,2,4$. The universal Askey--Wilson algebra $\triangle_q$ is a unital associative $\mathbb F$-algebra defined ... More

New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifoldsJun 04 2019Quantum toroidal algebras are obtained from quantum affine algebras by a further affinization, and, like the latter, can be used to construct integrable systems. These algebras also describe the symmetries of instanton partition functions for 5D $\mathcal{N}=1$ ... More

Twisted Representation of Algebra of $q$-Difference Operators, Twisted $q$-$W$ Algebras and Conformal BlocksJun 03 2019We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with nontrivial slope $n'/n$. As a vector space, it is naturally identified with ... More

Glueing vertex algebrasMay 31 2019Let $\mathsf{U}$ and $\mathsf{V}$ be vertex operator algebras with module (sub)categories $\mathcal{U}$ and $\mathcal{V}$, respectively, satisfying suitable assumptions which hold for example if $\mathcal{U}$ and $\mathcal{V}$ are semisimple rigid braided ... More

A Universal HKR TheoremMay 31 2019In this work we study the failure of the HKR theorem over rings of positive and mixed characteristic. For this we construct a \emph{filtered circle} interpolating between the usual topological circle and a formal version of it. By mapping to schemes we ... More

Generators, spanning sets and existence of twisted modules for a grading-restricted vertex (super)algebraMay 30 2019For a grading-restricted vertex superalgebra $V$ and an automorphism $g$ of $V$, we give a linearly independent set of generators of the universal lower-bounded generalized $g$-twisted $V$-module $\widehat{M}^{[g]}_{B}$ constructed by the author. We prove ... More

Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. III. Factorized asymptoticsMay 30 2019In the two preceding parts of this series of papers, we introduced and studied a recursion scheme for constructing joint eigenfunctions $J_N(a_+, a_-,b;x,y)$ of the Hamiltonians arising in the integrable $N$-particle systems of hyperbolic relativistic ... More

New Solutions to the Reflection Equation with BracesMay 29 2019The reflection equation of Cherednik is a counterpart to the celebrated Yang-Baxter equation, with importance in the theory of integrable systems. We obtain several new solutions of the reflection equation using braces building on the work of Smoktunowicz, ... More

New Solutions to the Reflection Equation with BracesMay 29 2019Jun 05 2019The reflection equation of Cherednik is a counterpart to the celebrated Yang-Baxter equation, with importance in the theory of integrable systems. We obtain several new solutions of the reflection equation using braces building on the work of Smoktunowicz, ... More

The $κ$-(A)dS noncommutative spacetimeMay 29 2019The (3+1)-dimensional $\kappa$-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the $\kappa$-(A)dS Poisson homogeneous space. Under minimal physical assumptions, it is explicitly proven that ... More

The 2-Calabi-Yau property for multiplicative preprojective algebrasMay 28 2019We prove that multiplicative preprojective algebras, defined by Crawley-Boevey and Shaw, are 2-Calabi-Yau algebras for quivers containing an unoriented cycle. We also prove that the dg versions of these algebras (arising in Fukaya categories of certain ... More

Kawada-Itô-Kelley Theorem for Quantum SemigroupsMay 28 2019Idempotent states on locally compact quantum semigroups with weak cancellation properties are shown to be Haar states on a certain sub-object described by an operator system with comultiplication. We also give a characterization of the situation when ... More

Double quasi-Poisson brackets : fusion and new examplesMay 27 2019We exhibit new examples of double quasi-Poisson brackets, based on some classification results and the method of fusion. This method was introduced by Van den Bergh for a large class of double quasi-Poisson brackets which are said differential, and our ... More

A closer look at Kadeishvili's theoremMay 26 2019We give a proof of the Homotopy Transfer Theorem following Kadeishvili's original strategy. Although Kadeishvili originally restricted himself to transferring a dg algebra structure to an $A_\infty$-structure on homology, we will see that a small modification ... More

Covariant Differential Calculus Over Monoidal Hom-Hopf AlgebrasMay 25 2019Concepts of first order differential calculus (FODC) on a monoidal Hom-algebra and left-covariant FODC over a left Hom-quantum space with respect to a monoidal Hom-Hopf algebra are presented. Then, extension of the universal FODC over a monoidal Hom-algebra ... More

Centralizers of the superalgebra osp(1|2): the Brauer algebra as a quotient of the Bannai-Ito algebraMay 24 2019We provide an explicit isomorphism between a quotient of the Bannai--Ito algebra and the Brauer algebra. We clarify also the connection with the action of the Lie superalgebra osp(1|2) on the threefold tensor product of its fundamental representation. ... More

Convolution identities for Dunkl orthogonal polynomials from the $\mathfrak{osp}(1|2)$ Lie superalgebraMay 24 2019New convolution identities for orthogonal polynomials belonging to the $q=-1$ analog of the Askey-scheme are obtained. A specialization of the Chihara polynomials will play a central role as the eigenfunctions of a special element of the Lie superalgebra ... More

Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $M_{23}$May 23 2019Borcherds-Kac-Moody algebras generalise finite-dimensional, simple Lie algebras. Scheithauer showed that there are exactly ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight ... More

The Moore Complex of a Simplicial Cocommutative Hopf AlgebraMay 23 2019We introduce the Moore complex of a simplicial cocommutative Hopf algebra through Hopf kernels. The most striking result to emerge from this construction is the coherent definition of 2-crossed modules of cocommutative Hopf algebras. This unifies the ... More

Condensations in higher categoriesMay 23 2019We present a higher-categorical generalization of the "Karoubi envelope" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is the closure for absolute limits. Our construction replaces ... More

Anomaly cancellation in the topological stringMay 22 2019We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira-Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for open-closed topological B-model. At one loop this anomaly cancellation ... More

A note on étale atlases for Artin stacks, Poisson structures and quantisationMay 22 2019We explain how any Artin stack $\mathfrak{X}$ over $\mathbb{Q}$ extends to a functor on non-negatively graded commutative cochain algebras, which we think of as functions on Lie algebroids or stacky affine schemes. There is a notion of \'etale morphisms ... More

Non-commutative deformation of Chern-Simons theoryMay 21 2019The problem of the consistent definition of gauge theories living on the non-commutative (NC) spaces with a non-constant NC parameter $\Theta(x)$ is discussed. Working in the L$_\infty$ formalism we specify the undeformed theory, $3$d abelian Chern-Simons, ... More

GL(NM) quantum dynamical $R$-matrix based on solution of the associative Yang-Baxter equationMay 21 2019In this letter we construct ${\rm GL}_{NM}$-valued dynamical $R$-matrix by means of unitary skew-symmetric solution of the associative Yang-Baxter equation in the fundamental representation of ${\rm GL}_{N}$. In $N=1$ case the obtained answer reproduces ... More

GL(NM) quantum dynamical $R$-matrix based on solution of the associative Yang-Baxter equationMay 21 2019Jun 18 2019In this letter we construct ${\rm GL}_{NM}$-valued dynamical $R$-matrix by means of unitary skew-symmetric solution of the associative Yang-Baxter equation in the fundamental representation of ${\rm GL}_{N}$. In $N=1$ case the obtained answer reproduces ... More