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Pointed Hopf actions on central simple division algebrasJul 18 2019We examine actions of finite-dimensional pointed Hopf algebras on central simple division algebras in characteristic 0. (By a Hopf action we mean a Hopf module algebra structure.) In all examples considered, we show that the given Hopf algebra does admit ... More
On the Galois correspondence for Hopf Galois structures arising from finite radical algebras and Zappa-Szép productsJul 17 2019Let $L/K$ be a $G$-Galois extension of fields with an $H$-Hopf Galois structure of type $N$. We study the ratio $GC(G, N)$, which is the number of intermediate fields $E$ with $K \subseteq E \subseteq L$ that are in the image of the Galois correspondence ... More
Tor-pairs: products and approximationsJul 17 2019Recently the author has studied rings for which products of flat modules have finite flat dimension. In this paper we extend the theory to characterize when products of modules in $\mathcal T$ have finite $\mathcal T$-projective dimension, where $\mathcal ... More
Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebrasJul 17 2019In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in the Lie-center, call them Lie-central derivations. We ... More
Sylvester operators on slice semi-regular functionsJul 17 2019The aim of this paper is to study a family of linear operators which are built from left and right $*$-multiplication on the space of slice semi-regular functions $\mathcal{RM}(\Omega)$ on a circular domain $\Omega$ contained in the skew-symmetric algebra ... More
Finite-dimensional differential graded algebras and their geometric realizationsJul 16 2019We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with a full separable ... More
Dedekind semidomainsJul 16 2019We define Dedekind semidomains as semirings in which each nonzero fractional ideal is invertible. Then we find some equivalent condition for semirings to being Dedekind. For example, we prove that a Noetherian semidomain is Dedekind if and only if it ... More
Actions of cocommutative Hopf algebrasJul 16 2019Let $H$ be a cocommutative Hopf algebra acting on an algebra $A$. Assuming the base field to be algebraically closed and the $H$-action on $A$ to be integral, that is, it is given by a coaction of some Hopf subalgebra of the finite dual $H^\circ$ that ... More
Spectral properties for a type of heptadiagonal symmetric matricesJul 16 2019In this paper we express the eigenvalues of a sort of real heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From these prescribed eigenvalues we compute also eigenvectors ... More
Involutions on Incidence Algebras of Finite PosetsJul 16 2019We give various formulas to compute the number of all involutions, i.e. elements of order 2, in an incidence algebra $I(X,\mathbb{K})$, where $X$ is a finite poset (star, Y and Rhombuses) and $\mathbb{K}$ is a finite field of characteristic different ... More
Semisimple Reflection Hopf Algebras of Dimension SixteenJul 15 2019For each nontrivial semisimple Hopf algebra $H$ of dimension sixteen over $\mathbb{C}$, the smallest dimension inner-faithful representation of $H$ acting on a quadratic AS regular algebra $A$ of dimension 2 or 3, homogeneously and preserving the grading, ... More
On the Noether Bound for Noncommutative RingsJul 15 2019We present two noncommutative algebras over a field of characteristic zero that each posses a family of actions by cyclic groups of order $2n$, represented in $n \times n$ matrices, requiring generators of degree $3n$.
Topological rewriting systems applied to standard bases and syntactic algebrasJul 15 2019We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting systems with ... More
Ordinal sums of triangular norms on a bounded latticeJul 15 2019The ordinal sum construction provides a very effective way to generate a new triangular norm on the real unit interval from existing ones. One of the most prominent theorems concerning the ordinal sum of triangular norms on the real unit interval states ... More
Pentagonal quasigroups, their translatability and parastrophesJul 14 2019Any pentagonal quasigroup is proved to have the product xy = R(x)+y-R(y) where (Q,+) is an Abelian group, R is its regular automorphism satisfying R^4-R^3+R^2-R+1 = 0 and 1 is the identity mapping. All abelian groups of order n<100 inducing pentagonal ... More
On k-Noetherian and k-Artinian SemiringsJul 13 2019We investigate left k-Noetherian and left k-Artinian semirings. We characterize such semirings using i-injective semimodules. We prove in particular, a partial version of the celebrated Bass-Papp Theorem for semiring. We illustrate our main results by ... More
Flat Semimodules & von Neumann Regular SemiringsJul 13 2019Flat modules play an important role in the study of the category of modules over rings and in the characterization of some classes of rings. We study the e-flatness for semimodules introduced by the first author using his new notion of exact sequences ... More
Integrality over ideal semifiltrationsJul 13 2019We study integrality over rings (all commutative in this paper) and over ideal semifiltrations (a generalization of integrality over ideals). We begin by reproving classical results, such as a version of the "faithful module" criterion for integrality ... More
An introduction to Mathieu subspacesJul 13 2019This is the note for the four lectures given by the author in the ``International Short-School/Conference on Affine Algebraic Geometry and the Jacobian Conjecture" at Chern Institute of Mathematics, Nankai University, Tianjin, China. July 14-25, 2014. ... More
Mathieu-Zhao spaces of polynomial ringsJul 13 2019We describe all Mathieu-Zhao spaces of $k[x_1,\cdots,x_n]$ ($k$ is an algebraically closed field of characteristic zero) which contains an ideal of finite codimension. Furthermore we give an algorithm to decide if a subspace of the form $I+kv_1+\cdots+kv_r$ ... More
Cohomology and linear deformation of BiHom-left-symmetric algebrasJul 13 2019The aim of this work is to introduce representations of BiHom-left-symmetric algebras. and develop its cohomology theory. As applications, we study linear deformations of BiHom-left-symmetric algebras, which are characterized by its second cohomology ... More
Semimodules over commutative semirings and modules over unitary commutative ringsJul 13 2019We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and submodules. In the ... More
Filiform Lie algebras with low derived lengthJul 12 2019We construct, for any integer n greater than or equal to 5, a family of complex filiform Lie algebras with derived length at most 3 and dimension n. We also give examples of n-dimensional filiform Lie algebras with derived length greater than 3.
Cograde conditions and cotorsion pairsJul 12 2019Let $R$ and $S$ be rings and $_R\omega_S$ a semidualizing bimodule. We study when the double functor $\Tor^S_i(\omega, \Ext^i_{R}(\omega,-))$ preserves epimorphisms and the double functor $\Ext_{R}^i(\omega, \Tor_i^{S}(\omega,-))$ preserves monomorphisms ... More
Covers and direct limits: A contramodule-based approachJul 12 2019We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits, both in the categorical tilting context and beyond. In the $n$-tilting-cotilting correspondence situation, if $\mathsf A$ is a Grothendieck abelian ... More
Nearly Frobenius AlgebrasJul 11 2019In this introductory paper we study nearly Frobenius algebras which are generalizations of the concept of a Frobenius algebra which appear naturally in topology: nearly Frobenius algebras have no traces (co-units). We survey the most basic foundational ... More
On a special presentation of matrix algebrasJul 11 2019Recognizing when a ring is a complete matrix ring is of significant importance in algebra. It is well-known folklore that a ring $R$ is a complete $n\times n$ matrix ring, so $R\cong M_{n}(S)$ for some ring $S$, if and only if it contains a set of $n\times ... More
Invariants of formal pseudodifferential operator algebras and algebraic modular formsJul 11 2019We study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to some canonical ... More
Simple-minded reductions of triangulated categoriesJul 11 2019We will introduce a new reduction process of triangulated category, which is analogue to the silting reduction and Calabi-Yau reduction. For a triangulated category $\cal T$ with a pre-simple-minded collection (=pre-SMC) $\cal R$, we construct a new triangulated ... More
Word problem for finitely presented metabelian Poisson algebrasJul 11 2019We first construct a linear basis for a free metabelian Poisson algebra generated by an arbitrary well-ordered set. It turns out that such a linear basis depends on the characteristic of the underlying field. Then we elaborate the method of Gr\"{o}bner--Shirshov ... More
Gröbner--Shirshov bases for commutative dialgebrasJul 11 2019We establish Gr\"obner--Shirshov bases theory for commutative dialgebras. We show that for any ideal $I$ of $Di[X]$, $I$ has a unique reduced Gr\"obner--Shirshov basis, where $Di[X]$ is the free commutative dialgebra generated by a set $X$, in particular, ... More
Rigid Lie algebras and algebraicityJul 11 2019The notion of rigidity of Lie algebra is linked to the following problem: when does a Lie brackets $\mu$ on a vector space g satisfy that every Lie bracket $\mu_1$ sufficiently close to $\mu$ is of the form $\mu_1 = P.\mu $ for some P in GL(g) close to ... More
Matlis category equivalences for a ring epimorphismJul 11 2019Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism $u\colon R\to U$. Assuming that the ring epimorphism is homological of flat/projective dimension $1$, we discuss the abelian categories ... More
On the tilting complexes for the Auslander algebra of the truncated polynomial ringJul 10 2019We give a bijection between the tilting complexes in the bounded homotopy category of the Auslander algebra of the truncated polynomial ring and ZxB where B is the Artin braid goup of type A with n-1 generators. The tilting complexes have mutation components ... More
Minimal semi-flat-cotorsion replacements and cosupportJul 10 2019Over a commutative noetherian ring $R$ of finite Krull dimension, we show that every complex of flat cotorsion $R$-modules decomposes as a direct sum of a minimal complex and a contractible complex. Moreover, we define the notion of a semi-flat-cotorsion ... More
A functorial approach to monomorphism categories for species IJul 10 2019For any generalised species over a locally bounded quiver we investigate abstract versions of the monomorphism category as studied by Ringel and Schmidmeier. We prove that analogues of the kernel and cokernel functor send almost split sequences over the ... More
Stability in graded rings associated with commutative augmented ringsJul 10 2019Let $A$ be a commutative augmented ring and $I$ be its augmentation ideal. This paper shows that the sequence $\{I^n/I^{n+1}\}$ becomes stationary up to isomorphism. The result yields stability in the associated graded ring of $A$ along $I$.
Split Hopf algebras, quasi-shuffle algebras, and the cohomology of Omega Sigma XJul 09 2019Let A and B be two connected graded commutative k-algebras of finite type, where k is a perfect field of positive characteristic p. We prove that the quasi--shuffle algebras generated by A and B are isomorphic as Hopf algebras if and only if A and B are ... More
Factorization of noncommutative polynomials and Nullstellensätze for the free algebraJul 09 2019This article gives a class of Nullstellens\"atze for noncommutative polynomials. The singularity set of a noncommutative polynomial $f=f(x_1,\dots,x_g)$ is $Z(f)=(Z_n(f))_n$, where $Z_n(f)=\{X \in M_n^g: \det f(X) = 0\}.$ The first main theorem of this ... More
Leonard pairs, spin models, and distance-regular graphsJul 08 2019Jul 17 2019A Leonard pair is an ordered pair of diagonalizable linear maps on a finite-dimensional vector space, that each act on an eigenbasis for the other one in an irreducible tridiagonal fashion. In the present paper we consider a type of Leonard pair, said ... More
Leonard pairs, spin models, and distance-regular graphsJul 08 2019A Leonard pair is an ordered pair of diagonalizable linear maps on a finite-dimensional vector space, that each act on an eigenbasis for the other one in an irreducible tridiagonal fashion. In the present paper we consider a type of Leonard pair, said ... More
On Higher {g_n, h_n}-derivationsJul 08 2019In this article, we introduce the concepts of higher {g_n, h_n}-derivation and Jordan higher {g_n, h_n}-derivation, and then we give a characterization of higher {g_n, h_n}-derivations in terms of {g, h}-derivations. Using this result, we prove that every ... More
Commutative Lie algebras and commutative cohomology in characteristic $2$Jul 08 2019We discuss a version of the Chevalley--Eilenberg cohomology in characteristic $2$, where the alternating cochains are replaced by symmetric ones.
The Realization Problem for Finitely Generated Refinement MonoidsJul 08 2019We show that every finitely generated conical refinement monoid can be represented as the monoid $\mathcal V(R)$ of isomorphism classes of finitely generated projective modules over a von Neumann regular ring $R$. To this end, we use the representation ... 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
Pseudo-dualizing complexes of bicomodules and pairs of t-structuresJul 07 2019This paper is a coalgebra version of arXiv:1703.04266 and a sequel to arXiv:1607.03066. We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras $\mathcal C$ and $\mathcal D$. For any such complex ... More
Is supernilpotence super nilpotence?Jul 07 2019We show that the answer to the question in the title is: ``Yes, for finite algebras.''
Is supernilpotence super nilpotence?Jul 07 2019Jul 14 2019We show that the answer to the question in the title is: ``Yes, for finite algebras.''
Weighted Leavitt path algebras that are isomorphic to unweighted Leavitt path algebrasJul 05 2019Let $K$ be a field. We characterise the row-finite weighted graphs $(E,w)$ such that the weighted Leavitt path algebra $L_K(E,w)$ is isomorphic to an unweighted Leavitt path algebra. Moreover, we prove that if $L_K(E,w)$ is locally finite, or Noetherian, ... More
A Commutative Algebra Approach to Multiplicative Hom-Lie AlgebrasJul 04 2019We use a method of commutative algebra to describe the affine variety $\textrm{HLie}_{m}(\mathfrak{gl}_{n}(\mathbb{C}))$ of all multiplicative Hom-Lie algebras on the general linear Lie algebra $\mathfrak{gl}_{n}(\mathbb{C})$, showing that $\textrm{HLie}_{m}(\mathfrak{gl}_{2}(\mathbb{C}))$ ... More
Extensions of finite irreducible modules of Lie conformal algebras $\mathcal{W}(a,b)$ and some Schrödinger-Virasoro type Lie conformal algebrasJul 04 2019Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we give a complete classification of extensions of finite irreducible conformal modules ... 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
Frobenius-Perron theory for projective schemesJul 04 2019The Frobenius-Perron theory of an endofunctor of a $\Bbbk$-linear category (recently introduced in [CG]) provides new invariants for abelian and triangulated categories. Here we study Frobenius-Perron type invariants for derived categories of commutative ... More
The universal enveloping algebra of $\mathfrak{sl}_2$ and the Racah algebraJul 03 2019Let $\mathbb{F}$ denote a field with ${\rm char\,}\mathbb{F}\not=2$. The Racah algebra $\Re$ is the unital associative $\mathbb{F}$-algebra defined by generators and relations in the following way. The generators are $A$, $B$, $C$, $D$. The relations ... More
Minus Partial Order in Regular ModulesJul 03 2019The minus partial order is already known for sets of matrices over a field and bounded linear operators on arbitrary Hilbert spaces. Recently, this partial order has been studied on Rickart rings. In this paper, we extend the concept of the minus relation ... More
On the growth of algebras, semigroups, and hereditary languagesJul 03 2019We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.
Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relationsJul 02 2019Jul 03 2019We establish and explore a relationship between two approaches to moment-cumulant relations in free probability theory: on one side the main approach, due to Speicher, given in terms of M\"obius inversion on the lattice of noncrossing partitions, and ... More
Some $q$-exponential formulas involving the double lowering operator $ψ$ for a tridiagonal pairJul 02 2019Let $\mathbb{K}$ denote an algebraically closed field and let $V$ denote a vector space over $\mathbb{K}$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$. We assume that $A,A^*$ belongs to a family of tridiagonal pairs said ... More
Automorphism-Liftable ModulesJul 01 2019In this paper, we describe all automorphism-liftable torsion modules over non-primitive hereditary Noetherian prime rings. We also study automorphism-liftable non-torsion modules over not necessarily commutative Dedekind prime rings
Uniserial Noetherian Centrally Essential RingsJul 01 2019Jul 04 2019It is proved that a ring $R$ is a right uniserial, right Noetherian centrally essential ring if and only if $R$ is a commutative discrete valuation domain or a left and right Artinian, left and right uniserial ring. It is also proved that there exist ... More
Uniserial Noetherian Centrally Essential RingsJul 01 2019It is proved that a ring $R$ is a right uniserial, right Noetherian centrally essential ring if and only if $R$ is a commutative discrete valuation domain or a left and right Artinian, left and right uniserial ring. It is also proved that there exist ... More
Degenerations of nilpotent associative commutative algebrasJul 01 2019We give a complete description of degenerations of complex $5$-dimensional nilpotent associative commutative algebras.
Directed Graphs of Cayley FunctionsJul 01 2019In this paper we describe a condition under which a given function that commute with an idempotent function on an infinite set is a Cayley function using its functional digraph.
Another characterization of congruence distributive varietiesJun 30 2019We provide a Maltsev characterization of congruence distributive varieties by showing that a variety $\mathcal {V}$ is congruence distributive if and only if the congruence identity $\alpha \cap (\beta \circ \gamma \circ \beta ) \subseteq \alpha \beta ... More
Topological linear spaces of formal linear sums and continuous linear operatorsJun 30 2019The rings of linear continuous operators on the topological spaces of $\mathfrak{G}$-zero maps were described, where $\mathfrak{G}$ is a filter on a set with an involution. This applies to modules of formal series with well ordered support over left ordered ... More
Spectral properties of anti-heptadiagonal persymmetric Hankel matricesJun 29 2019In this paper we express the eigenvalues of anti-heptadiagonal persymmetric Hankel matrices as the zeros of explicit polynomials giving also a representation of its eigenvectors. We present also an expression depending on localizable parameters to compute ... More
A unified approach to Leavitt path algebrasJun 29 2019We define Cohn-Leavitt path algebras $\mathcal{A}_K(\dot{E})$ of a new class of graphs called $\mathcal{A}$-graphs $\dot{E}$, which generalize the constructions of Leavitt path algebras of various types of graphs. We compute Gr\"ober-Shirshov basis of ... More
Classification of 3-Dimensional BiHom-Associative and BiHom-BialgebrasJun 28 2019The purpose of this paper is to study the structure and the algebraic varieties of BiHom-associative algebras. We provide a classication of n-dimensional BiHom-associative and BiHom-bialgebras and BiHom Hopf algebras for n $\le$ 3.
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
Synchronicity phenomenon in cluster patternsJun 28 2019Jul 10 2019It has been known that several objects such as cluster variables, coefficients, seeds, and $Y$-seeds in different cluster patterns with common exchange matrices share the same periodicity under mutations. We call it synchronicity phenomenon in cluster ... More
Synchronicity phenomenon in cluster patternsJun 28 2019It has been known that several objects such as cluster variables, coefficients, seeds, and $Y$-seeds in different cluster patterns with common exchange matrices share the same periodicity under mutations. We call it synchronicity phenomenon in cluster ... More
One hundred twenty-seven subsemilattices and planarityJun 28 2019Let $L$ be a finite $n$-element semilattice. We prove that if $L$ has at least $127\cdot 2^{n-8}$ sublattices, then $L$ is planar. For $n>8$, this result is sharp since there is a non-planar semilattice with exactly $127\cdot 2^{n-8}-1$ sublattices.
One hundred twenty-seven subsemilattices and planarityJun 28 2019Jul 01 2019Let $L$ be a finite $n$-element semilattice. We prove that if $L$ has at least $127\cdot 2^{n-8}$ subsemilattices, then $L$ is planar. For $n>8$, this result is sharp since there is a non-planar semilattice with exactly $127\cdot 2^{n-8}-1$ subsemilattices. ... More
The Nakayama automorphism of a self-injective preprojective algebraJun 27 2019We give a simple proof, using Auslander-Reiten theory, that the preprojective algebra of a basic hereditary algebra of finite representation type is Frobenius. We then describe its Nakayama automorphism, which is induced by the Nakayama functor on the ... More
The Racah algebra as a subalgebra of the Bannai--Ito algebraJun 27 2019Assume that $\mathbb F$ is a field with ${\rm char\,}\mathbb F\not=2$. The Racah algebra $\Re$ is a unital associative $\mathbb F$-algebra defined by generators and relations. The generators are $A,B,C,D$ and the relations assert that $$ [A,B]=[B,C]=[C,A]=2D ... More
The Racah algebra as a subalgebra of the Bannai--Ito algebraJun 27 2019Jun 28 2019Assume that $\mathbb F$ is a field with ${\rm char\,}\mathbb F\not=2$. The Racah algebra $\Re$ is a unital associative $\mathbb F$-algebra defined by generators and relations. The generators are $A,B,C,D$ and the relations assert that $$ [A,B]=[B,C]=[C,A]=2D ... More
On the Sparseness of Certain MRD CodesJun 27 2019We determine the proportion of $[3\times 3;3]$-MRD codes over ${\mathbb F}_q$ within the space of all $3$-dimensional rank-metric codes over the same field. This shows that these MRD codes are sparse in the sense that this proportion tends to $0$ as $q\rightarrow\infty$. ... More
Irreducible and permutative representations of ultragraph Leavitt path algebrasJun 27 2019We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt path algebras Chen's construction of irreducible representations of Leavitt path algebras. We ... More
The normal shapes of the symplectic and contact forms over algebras of divided powersJun 27 2019This text is the English translation of a 1986 manuscript which gives the classification of the differential forms parametrizing the finite-dimensional Lie algebras of hamiltonian and contact Cartan types over fields of positive characteristic. The results ... More
Some extensions of quaternions and symmetries of simply connected space formsJun 26 2019It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the groups of unit--norm ... More
Decompositions of algebras and post-associative algebra structuresJun 24 2019We introduce post-associative algebra structures and study their relationship to post-Lie algebra structures, Rota--Baxter operators and decompositions of associative algebras and Lie algebras. We show several results on the existence of such structures. ... More
The Schwarz-Voronov embedding of $\mathbb{Z}_2^n$-manifoldsJun 24 2019Informally, $\mathbb{Z}_2^n$-manifolds are `manifolds' with $\mathbb{Z}_2^n$-graded coordinates and a sign rule determined by the standard scalar product of their $\mathbb{Z}_2^n$-degrees. Such manifolds can be understood in a sheaf-theoretic framework, ... More
Description of unitary representations of the group of infinite $p$-adic integer matricesJun 22 2019We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of infinite matrices ... More
Supernilpotent Taylor algebras are nilpotentJun 21 2019We develop the theory of the higher commutator for Taylor varieties. A new higher commutator operation called the hypercommutator is defined using a type of invariant relation called a higher dimensional congruence. The hypercommutator is shown to be ... More
Supernilpotent Taylor algebras are nilpotentJun 21 2019Jun 24 2019We develop the theory of the higher commutator for Taylor varieties. A new higher commutator operation called the hypercommutator is defined using a type of invariant relation called a higher dimensional congruence. The hypercommutator is shown to be ... More
Manin triples of 3-Lie algebras induced by involutive derivationsJun 21 2019For any $n$-dimensional 3-Lie algebra $A$ over a field of characteristic zero with an involutive derivation $D$, we investigate the structure of the 3-Lie algebra $B_1=A\ltimes_{ad^*} A^* $ associated with the coadjoint representation $(A^*, ad^*)$. We ... More
On chains and Rota-Baxter operators of evolution algebrasJun 19 2019The paper is devoted to study new classes of chains of evolution algebras and their time-depending dynamics. Moreover, we construct some Rote-Baxter operators of such algebras.
The tight groupoid of the inverse semigroups of left cancellative small categoriesJun 18 2019We fix a path model for the space of filters of the inverse semigroup $\mathcal{S}_\Lambda$ associated to a left cancellative small category $\Lambda$. Then, we compute its tight groupoid, thus giving a representation of its $C^*$-algebra as a (full) ... More
Pre-Calabi-Yau algebras and double Poisson bracketsJun 17 2019We give an explicit formula showing how the double Poisson algebra introduced in \cite{VdB} appears as a particular part of a pre-Calabi-Yau structure, i.e. cyclically invariant, with respect to the natural inner form, solution of the Maurer-Cartan equation ... More
Étale groupoid algebras with coefficients in a sheaf and skew inverse semigroup ringsJun 17 2019Given an action $\varphi$ of of inverse semigroup $S$ on a ring $A$ (with domain of $\varphi(s)$ denoted by $D_{s^*}$) we show that if the ideals $D_e$, with $e$ an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$ can be realized ... More
Leavitt path algebras over a poset of fieldsJun 17 2019Let $E$ be a finite directed graph, and let $I$ be the poset obtained as the antisymmetrization of its set of vertices with respect to a pre-order $\le$ that satisfies $v\le w$ whenever there exists a directed path from $w$ to $v$. Assuming that $I$ is ... More
Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularityJun 17 2019We study properties of graded maximal Cohen-Macaulay modules over an N-graded locally finite, Auslander Gorenstein, and Cohen-Macaulay algebra of dimension two. As a consequence, we extend a part of McKay correspondence in dimension two to a more general ... More
3-Lie bialgebras and 3-pre-Lie algebras induced by involutive derivationsJun 16 2019In this paper, we study the structure of 3-Lie algebras with involutive derivations. We prove that if $A$ is an $m$-dimensional 3-Lie algebra with an involutive derivation $D$, then there exists a compatible 3-pre-Lie algebra $(A, \{ , , , \}_D)$ such ... More
Quadratic $D$-forms with applications to hermitian formsJun 15 2019We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extension of that field. Some generalized notions of isotropy, metabolicity and ... 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
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
Time warping invariants of multidimensional time seriesJun 13 2019In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe ... More
Smooth digraphs modulo primitive positive constructabilityJun 13 2019We consider the poset that arises from ordering finite smooth digraphs via pp-constructability. We give a complete description of this poset and, in particular, we prove that it is a distributive lattice. Moreover, we show that in order to separate two ... More
Sectional algebras of semigroupoid bundlesJun 13 2019In this article we use semigroupoids to describe a notion of algebraic bundles, mostly motivated by Fell ($C^*$-algebraic) bundles, and the sectional algebras associated to them. As the main motivational example, Steinberg algebras may be regarded as ... More
Higher extensions for gentle algebrasJun 12 2019In this paper we determine extensions of higher degree between indecomposable modules over gentle algebras. In particular, our results show how such extensions either eventually vanish or become periodic. We give a geometric interpretation of vanishing ... More