Latest in math.ra

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A Control Theorem for Primitive ideals in Iwasawa algebrasSep 17 2019Let p be a prime, K a p-adic field, G a nilpotent, uniform pro-p group. We prove that all faithful, primitive ideals in the Iwasawa algebra KG are controlled by the centraliser of the second term in the upper central series for G.
The eigenspaces of twisted polynomials over cyclic field extensionsSep 17 2019Let $R=K[t;\sigma]$, where $K/F$ is a field extension and $ \sigma $ an automorphism of $K$. We study the eigenspace of a skew polynomial $f\in K[t;\sigma]$ employing methods from nonassociative algebra, and obtain lower bounds on its dimension. When ... More
On the matrix equation $XB=BY$Sep 17 2019Let $G$ be a finite group of order $n$. In this paper we use rational homotopy theory to define a matrix $B_{G}=[b_{ij}]$, where $b_{ij}\in\{0,1\}$, such that $G$ is isomorphic to a certain subgroup of $\mathrm{GL}(\frac{n^2+n+4}{2},\Bbb Q)\times \mathrm{GL}(n,\Bbb ... More
The Kostant invariant and special $ε$-orthogonal representations for $ε$-quadratic colour Lie algebrasSep 16 2019Let k be a field of characteristic not two or three, let $\mathfrak{g}$ be a finite-dimensional colour Lie algebra and let V be a finite-dimensional representation of $\mathfrak{g}$. In this article we give various ways of constructing a colour Lie algebra ... More
Efficient Rational Creative TelescopingSep 15 2019We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approach, our algorithm has the nice feature that the computation of a telescoper is independent of its certificate. ... More
The $A$-fibered Burnside ring as $A$-fibered biset functor in characteristic zeroSep 14 2019Let $A$ be an abelian group and let $\mathbb{K}$ be a field of characteristic zero containing roots of unity of all orders equal to finite element orders in $A$. In this paper we prove foundational properties of the $A$-fibered Burnside ring functor $B_{\mathbb{K}}^A$ ... More
Fusion systems of blocks of finite groups over arbitrary fieldsSep 14 2019To any block idempotent $b$ of a group algebra $kG$ of a finite group $G$ over a field $k$ of characteristic $p>0$, Puig associated a fusion system and proved that it is saturated if the $k$-algebra $kC_G(P)e$ is split, where $(P,e)$ is a maximal $kGb$-Brauer ... More
Evaluations of noncommutative polynomials on finite dimensional algebras. L'vov-Kaplansky ConjectureSep 13 2019Sep 18 2019Let $p$ be a polynomial in several non-commuting variables with coefficients in an algebraically closed field $K$ of arbitrary characteristic. It has been conjectured that for any $n$, for $p$ multilinear, the image of $p$ evaluated on the set $M_n(K)$ ... More
Scalar $q$-subresultants and Dickson matricesSep 13 2019Following the ideas of Ore and Li we study $q$-analogues of scalar subresultants and show how these results can be applied to determine the rank of an $\mathbb{F}_q$-linear transformation $f$ of $\mathbb{F}_{q^n}$. As an application we show how certain ... More
2-local derivations on Witt algebrasSep 13 2019In this paper, we prove that every 2-local derivation on Witt algebras $W_n, W_n^+$ or $W_n^{++} $ is a derivation for all $n=1,2,\cdots,\infty$.
G. Czédli's tolerance factor lattice construction, and weak ordered relationsSep 13 2019The main results of the paper points out the connection between the weak ordered relations and factor lattices defined by tolerances. It is proved that for any tolerance $T$ of a lattice $L$ the Dedekind Mac-Neille completion of $L/T$ is isomorphic to ... More
Examples, counterexamples, and structure in bounded width algebrasSep 12 2019We study bounded width algebras which are minimal in the sense that every proper reduct does not have bounded width. We show that minimal bounded width algebras can be arranged into a pseudovariety with one basic ternary operation. We classify minimal ... More
Modules over trusses vs modules over rings: direct sums and free modulesSep 12 2019Categorical constructions on heaps and modules over trusses are considered and contrasted with the corresponding constructions on groups and rings. These include explicit description of free heaps and free Abelian heaps, coproducts or direct sums of Abelian ... More
The centralizer of an endomorphism over an arbitrary fieldSep 12 2019The centralizer of an endomorphism of a finite dimensional vector space is known when the endomorphism is nonderogatory or when its minimal polynomial splits over the field. It is also known for the real Jordan canonical form. In this paper we characterize ... More
Observables on synaptic algebrasSep 12 2019Synaptic algebras, introduced by D. Foulis, generalize different algebraic structures used so far as mathematical models of quantum mechanics: the traditional Hilbert space approach, order unit spaces, Jordan algebras, effect algebras, MV-algebras, orthomodular ... More
Weak comp algebras and cup products in secondary Hochschild cohomology of entwining structuresSep 12 2019We define the secondary Hochschild complex for an entwining structure over a commutative $k$-algebra $B$. We show that this complex carries the structure of a weak comp algebra. We obtain cup product structures and Hodge type decomposition for the secondary ... More
Semimodular $λ$-latticesSep 11 2019The concept of a $\lambda$-lattice was introduced by V. Sn\'a\v sel in order to generalize some lattice concepts for directed posets whose elements need not have suprema or infima. We extend the concept of semimodularity from lattices to $\lambda$-lattices ... More
Degenerations of 8-dimensional 2-step nilpotent Lie algebrasSep 10 2019In this work, we consider degenerations between 8-dimensional 2-step nilpotent Lie algebras over $\mathbb{C}$ and obtain the geometric classification of the variety $\mathcal{N}^2_8$.
Noncommutative tensor triangular geometrySep 10 2019We develop a general noncommutative version of Balmer's tensor triangular geometry that is applicable to arbitrary monoidal triangulated categories (M$\Delta$Cs). Insight from noncommutative ring theory is used to obtain a framework for prime, semiprime, ... More
Noncommutative analogues of a cancellation theorem of Abhyankar, Eakin, and HeinzerSep 09 2019Let $k$ be a field and let $A$ be a finitely generated $k$-algebra. The algebra $A$ is said to be cancellative if whenever $B$ is another $k$-algebra with the property that $A[x]\cong B[x]$ then we necessarily have $A\cong B$. An important result of Abhyankar, ... More
A Family of Almost Invertible Infinite MatricesSep 09 2019An algebraic analogue of the family of Fredholm operators is introduced for the family of row and column finite matrices, dubbed "Fredholm matrices." In addition, a measure is introduced which indicates how far a Fredholm matrix is from an invertible ... More
Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph $C^*$-algebrasSep 09 2019We show that the endomorphism ring of any nonzero finitely generated projective module over the Leavitt path algebra $L_K(E)$ of an arbitrary graph $E$ with coefficients in a field $K$ is isomorphic to a Steinberg algebra. This yields in particular that ... More
On the Size of Finite Rational Matrix SemigroupsSep 09 2019Let $n$ be a positive integer and $\mathcal M$ a set of rational $n \times n$-matrices such that $\mathcal M$ generates a finite multiplicative semigroup. We show that any matrix in the semigroup is a product of matrices in $\mathcal M$ whose length is ... More
Counting finite-dimensional algebras over finite fieldsSep 09 2019In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed dimension over a given finite field. We use this method to derive an explicit formula for the number of 2-dimensional algebras over a finite ... More
When mutually subisomorphic Baer modules are isomorphicSep 08 2019The Schr\"{o}der-Bernstein Theorem for sets is well known. The question of whether two subisomorphic algebraic structures are isomorphic to each other, is of interest. An $R$-module $M$ is said to satisfy the Schr\"{o}der-Bernstein (or SB) property if ... More
p-reduced multicomponent KP hierarchy and classical W-algebras W(gl_N,p)Sep 07 2019For each partition p of an integer N \geq 2, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present paper we show that any tau-function of the p-reduced r-component KP hierarchy ... More
When a quotient of a distributive lattice is a boolean algebraSep 06 2019In this article, we introduce a lattice congruence with respect to a nonempty ideal $I$ of a distributive lattice $L$ and a derivation $d$ on $L$ denoted by $\theta_I^d$. We investigate some necessary and sufficient conditions for the quotient algebra ... More
Representations for three-point Lie algebras of genus zeroSep 06 2019In this paper, we study representations for three-point Lie algebras of genus zero based on the Cox-Jurisich's presentations. We construct two functors which transform simple restricted modules with nonzero levels over the standard affine algebras into ... More
The R-transform as a power map and its generalisations to higher degreeSep 05 2019We give iterative constructions for irreducible polynomials over F_q of degree nt^r for all nonnegative integers r, starting from irreducible polynomials of degree n. The iterative constructions correspond modulo fractional linear transformations to compositions ... More
The decomposition theorems in Baer $*$-ringsSep 05 2019We show a general decomposition theorem in Baer *-rings. As a consequence the vast majority of decompositions known in the algebra of bounded Hilbert space operators are generalized to Baer *-rings. There are also results which are new in the algebra ... More
Ubiquitous Lie polynomials in a two-generator universal enveloping algebraSep 05 2019The universal enveloping algebra $\mathscr{U}$ of a two-dimensional nonabelian Lie algebra $L$ is a Lie algebra itself with the commutator as Lie bracket. There exists a presentation of $\mathscr{U}$ with generators $x,y$ and relation $xy-yx=x$ such that ... More
Exact Hochschild extensions and deformed Calabi-Yau completionsSep 05 2019We introduce the Hochschild extensions of dg algebras, which are $A_\infty$-algebras. We show that all exact Hochschild extensions are symmetric Hochschild extensions, more precisely, every exact Hochschild extension of a finite dimensional complete typical ... More
Gerstenhaber brackets on Hochschild cohomology of general twisted tensor productsSep 05 2019We present techniques for computing Gerstenhaber brackets on Hochschild cohomology of general twisted tensor product algebras. These techniques involve twisted tensor product resolutions and are based on recent results on Gerstenhaber brackets expressed ... More
Gerstenhaber brackets on Hochschild cohomology of general twisted tensor productsSep 05 2019Sep 06 2019We present techniques for computing Gerstenhaber brackets on Hochschild cohomology of general twisted tensor product algebras. These techniques involve twisted tensor product resolutions and are based on recent results on Gerstenhaber brackets expressed ... More
On Frobenius-Perron DimensionSep 04 2019We propose a notion of Frobenius-Perron dimension for certain free $\mathbb{Z}$-modules of infinite rank and compute it for the $\mathbb{Z}$-modules of finite dimensional complex representations of unitary groups with nonnegative dominant weights. The ... More
On the axiomatisability of the dual of compact ordered spacesSep 04 2019We provide a direct and elementary proof of the fact that the category of Nachbin's compact ordered spaces is dually equivalent to an Aleph_1-ary variety of algebras. Further, we show that Aleph_1 is a sharp bound: compact ordered spaces are not dually ... More
On the axiomatisability of the dual of compact ordered spacesSep 04 2019Sep 13 2019We provide a direct and elementary proof of the fact that the category of Nachbin's compact ordered spaces is dually equivalent to an Aleph_1-ary variety of algebras. Further, we show that Aleph_1 is a sharp bound: compact ordered spaces are not dually ... More
Reflective prolate-spheroidal operators and the KP/KdV equationsSep 03 2019Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special cases, leaving ... More
An inductive method for $\mathrm{OI}$-modulesSep 03 2019In this paper we introduce an inductive method to study $\mathrm{OI}$-modules presented in finite degrees, where $\mathrm{OI}$ is a skeleton of the category of finitely totally ordered sets and strictly increasing maps. As an application, we obtain an ... More
Mitschke's Theorem is sharpSep 02 2019A. Mitschke showed that a variety with an $m$-ary near-unanimity term has J\'onsson terms $t_0, \dots, t _{2m-4} $ witnessing congruence distributivity. We show that Mitschke's result is sharp. We also evaluate the best possible number of Day terms witnessing ... More
Convex topological algebras via linear vector fields and Cuntz algebrasSep 02 2019Realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is analogous to the classical Jordan-Schwinger map. ... More
Finite generation for Hochschild cohomology of Gorenstein monomial algebrasSep 01 2019We show that a finite dimensional monomial algebra satisfies the finite generation conditions of Snashall-Solberg for Hochschild cohomology if and only if it is Gorenstein. This gives, in the case of monomial algebras, the converse to a theorem of Erdmann-Holloway-Snashall-Solberg-Taillefer. ... More
Invariant theory and wheeled PROPsSep 01 2019We study the category of wheeled PROPs using tools from Invariant Theory. A typical example of a wheeled PROP is the mixed tensor algebra ${\mathcal V}=T(V)\otimes T(V^\star)$, where $T(V)$ is the tensor algebra on an $n$-dimensional vector space over ... More
A new family of homogeneous Einstein manifolds based on symplectic triple systemsAug 31 2019For each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved that this is ... More
Convolutions on the complex torusAug 30 2019"Quasi-elliptic" functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated and given by Eisenstein series. A related structure has ... More
Functorial Properties of the Reticulation of a Universal AlgebraAug 30 2019We continue the study of the reticulation of a universal algebra initiated in \cite{retic}, characterizing morphisms which admit an image through the reticulation and investigating the kinds of varieties that admit reticulation functors.
Kinematical superspacesAug 29 2019We classify $N{=}1$ $d=4$ kinematical and aristotelian Lie superalgebras with spatial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quaternionic formalism which makes rotational covariance manifest and simplifies many ... More
Split bounded extension algebras and Han's conjectureAug 29 2019A main purpose of this paper is to prove that the class of finite dimensional algebras which verify Han's conjecture is closed under split bounded extensions.
The core inverse and constrained matrix approximation problemAug 29 2019In this paper,we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse:\begin{align}\nonumber \left\|{Mx - b} \right\|_F=\min\ \ {\rm subject\ to} \ \ {x\in\mathcal{R}(M)} ,\end{align} where $M\in\mathbb{C}^{\texttt{CM}}_n$. ... More
Homogeneous completely simple semigroupsAug 28 2019A semigroup is completely simple if it has no proper ideals and contains a primitive idempotent. We say that a completely simple semigroup $S$ is a homogeneous completely simple semigroup if any isomorphism between finitely generated completely simple ... More
Comparison of two notions of weak crossed productAug 27 2019We compare the restriction to the context of weak Hopf algebras of the notion of crossed product with a Hopf algebroid introduced in \cite{BB} with the notion of crossed product with a weak Hopf algebra introduced in~\cite{AG}
Distributive Noetherian Centrally Essential RingsAug 27 2019It is proved that a ring $A$ is a right or left Noetherian, right distributive centrally essential ring if and only if $A=A_1\times\cdots\times A_n$, where each of the rings $A_i$ is either a commutative Dedekind domain or a uniserial Artinian centrally ... More
Ideals of graphs: finding a set of generatorsAug 26 2019In this paper, we consider homological properties of so-called graph ideals. Consider $\Gamma$ is a graph with vertices $t_1$, ..., $t_s$, without self-loops and multiple adjacencies. We can associate with such a graph an ideal $I({\Gamma})$ of polynomial ... More
Ideals of graphs: finding a set of generatorsAug 26 2019Aug 28 2019In this paper, we consider homological properties of so-called graph ideals. Consider $\Gamma$ is a graph with vertices $t_1$, ..., $t_s$, without self-loops and multiple adjacencies. We can associate with such a graph an ideal $I({\Gamma})$ of polynomial ... More
Cellular automata over algebraic structuresAug 26 2019Let $G$ be a group and $A$ a set equipped with a collection of finitary operations. We study cellular automata $\tau : A^G \to A^G$ that preserve the operations of $A^G$ induced componentwise from the operations of $A$. We establish that the set $\text{EndCA}(G;A)$, ... More
ERRATA CORRIGE: Intrinsic algebraic entropyAug 26 2019The notion of intrinsic algebraic entropy of an endomorphism of a given Abelian group has been recently introduced in [D. Dikranjan, A. Giordano Bruno, L. Salce, S. Virili, Intrinsic algebraic entropy, J. Pure Appl. Algebra 219 (2015) 2933-2961]. In this ... More
Commutators, matrices and an identity of CopelandAug 24 2019Given two elements $a$ and $b$ of a noncommutative ring, we express $\left( ba\right)^n$ as a "row vector times matrix times column vector" product, where the matrix is the $n$-th power of a matrix with entries $\dbinom{i}{j}\operatorname{ad}_a^{i-j}\left( ... More
Varieties of Nilpotent Lie Superalgebras of dimension $\leq 5$Aug 23 2019In this paper we study the varieties of nilpotent Lie superalgebras of dimension $\leq 5$. We provide the algebraic classification of these superalgebras and obtain the irreducible components in every variety. As a by product we construct rigid nilpotent ... More
Free Bertini's theorem and applicationsAug 23 2019The simplest version of Bertini's irreducibility theorem states that the generic fiber of a non-composite polynomial function is an irreducible hypersurface. The main result of this paper is its analog for a free algebra: if $f$ is a noncommutative polynomial ... More
Essential Dimension, Symbol Length and $p$-rankAug 23 2019We prove that the essential dimension of central simple algebras of degree $p^{\ell m}$ and exponent $p^m$ over fields of characteristic $p$ is at least $\ell+1$. We do this by observing that the $p$-rank of $F$ bounds the symbol length in $\operatorname{Br}_{p^m}(F)$ ... More
Structures and bimodules of simple Hom-alternative algebrasAug 23 2019This paper is mainly devoted to a structure study of Hom-alternative algebras . Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are displayed. Moreover some results about Hom-alternative bimodule are found.
Affine equivalence for quadratic rotation symmetric Boolean functionsAug 22 2019Let $f_n(x_0, x_1, \ldots, x_{n-1})$ denote the algebraic normal form (polynomial form) of a rotation symmetric (RS) Boolean function of degree $d$ in $n \geq d$ variables and let $wt(f_n)$ denote the Hamming weight of this function. Let $(0, a_1, \ldots, ... More
Residues of skew rational functions and linearized Goppa codesAug 22 2019This paper constitutes a first attempt to do analysis with skew polynomials. Precisely, our main objective is to develop a theory of residues for skew rational functions (which are, by definition, the quotients of two skew polynomials). We prove in particular ... More
An Efficient Algorithm for Latin Squares in a Bipartite Min-Max-Plus SystemAug 22 2019In this paper, we consider the eigenproblems for Latin squares in a bipartite min-max-plus system. The focus is upon developing a new algorithm to compute the eigenvalue and eigenvectors (trivial and non-trivial) for Latin squares in a bipartite min-max-plus ... More
In memory of Igor Dmitrievich AdoAug 22 2019We give a translation from Russian into English of the article "In memory of Igor Dmitrievich Ado" written by A.V. Dorodnov and I.I. Sakhaev and published in Izv.\ Vyssh.\ Uchebn.\ Zaved.\ Mat.\ no. 8, (1984), 87--88. It is an orbituary for I. D. Ado. ... More
Tropical Analysis of the Asymptotics of the Perron-Frobenius EigenvectorAug 22 2019Asymptotic properties of matrices are, in general, difficult to analyze with classical mathematical techniques. In very specific cases, there is a well-known connection between the asymptotic behavior of a matrix's leading eigenvector and the corresponding ... More
Idempotents and one-sided units II. Lattice invariants and a semigroup of functors on the category of monoidsAug 22 2019For a monoid $M$, we denote by $\mathbb G(M)$ the group of units, $\mathbb E(M)$ the submonoid generated by the idempotents, and $\mathbb G_L(M)$ and $\mathbb G_R(M)$ the submonoids consisting of all left or right units. Writing $\mathcal M$ for the (monoidal) ... More
Planar semilattices and nearlattices with eighty-three subnearlatticesAug 22 2019Finite (upper) nearlattices are essentially the same mathematical entities as finite semilattices, finite commutative idempotent semigroups, finite join-enriched meet semilattices, and chopped lattices. We prove that if an $n$-element nearlattice has ... More
Construction of Hopf algebroidsAug 21 2019For arbitrary algebras $L$, we construct Hopf algebroids $A_\sigma$ with base rings $L$ by means of $\sigma^{ab}_{cd}\in L$ satisfying suitable properties.
On Cores in Yetter-Drinfel'd Hopf AlgebrasAug 20 2019By constructing explicit examples, we show that the core of a group-like element in a cocommutative cosemisimple Yetter-Drinfel'd Hopf algebra over the group ring of a finite abelian group is not always completely trivial.
Matrices in companion rings, Smith forms, and the homology of 3-dimensional Brieskorn manifoldsAug 20 2019We study the Smith forms of matrices of the form $f(C_g)$ where $f(t),g(t)\in R[t]$, $C_g$ is the companion matrix of the (monic) polynomial $g(t)$, and $R$ is an elementary divisor domain. Prominent examples of such matrices are circulant matrices, skew-circulant ... More
A Normal form for HNN-extension of DialgebrasAug 19 2019We introduce an explicit Groebner-Shirshov basis for HNN-extension of dialgebras. On the basis of Composition-Diamond lemma, a normal form for the elements of HNN-extension of digebras will be determined.
Classification of multivariate skew polynomial rings over finite fields via affine transformations of variablesAug 19 2019In this work, free multivariate skew polynomial rings are considered, together with their quotients over ideals of skew polynomials that vanish at every point (which includes minimal multivariate skew polynomial rings). We provide a full classification ... More
On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2Aug 19 2019In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We generalize the approach ... More
$\mathbb Z Q$ type constructions in higher representation theoryAug 19 2019Let $Q$ be an acyclic quiver, it is classical that certain truncations of the translation quiver $\mathbb Z Q$ appear in the Auslander-Reiten quiver of the path algebra $kQ$. We introduce the $n$-translation quiver $\mathbb Z|_{n-1} Q$ as a generalization ... More
Poisson Dixmier-Moeglin equivalence from a topological point of viewAug 19 2019A complex affine Poisson algebra $A$ is said to satisfy the Poisson Dixmier-Moeglin equivalence if the Poisson cores of maximal ideals of $A$ are precisely those Poisson prime ideals that are locally closed in the Poisson prime spectrum ${\rm P. spec}\, ... More
Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate ringsAug 18 2019The elliptic algebras in the title are connected graded $\mathbb{C}$-algebras, denoted $Q_{n,k}(E,\tau)$, depending on a pair of relatively prime integers $n>k\ge 1$, an elliptic curve $E$, and a point $\tau\in E$. For fixed $n$ and $k$, they form a flat ... More
Modules over semisymmetric quasigroupsAug 18 2019The class of semisymmetric quasigroups is determined by the identity $(yx)y=x.$ We prove that the universal multiplication group of a semisymmetric quasigroup $Q$ is free over its underlying set and then specify the point-stabilizers of an action of this ... More
Cohomology of Burnside RingsAug 16 2019Let $G$ be a finite group and $A(G)$ its Burnside ring. For $H \subset G$ let $\mathbb{Z}_H$ denote the $A(G)$-module corresponding to the mark homomorphism associated to $H$. When the order of $G$ is square-free we give a complete description of the ... More
Primitive Idempotents and Constacyclic Codes over Finite Chain RingsAug 16 2019Let $R$ be a commutative local finite ring. In this paper, we construct the complete set of pairwise orthogonal primitive idempotents of $R[X]/<g>$ where $g$ is a regular polynomial in $R[X]$. We use this set to decompose the ring $R[X]/<g>$ and to give ... More
Pirashvili's conjecture on the Leibniz homology for Lie algebrasAug 16 2019We prove a conjecture of Pirashvili, which says that a non-trivial finite-dimensional complex Lie algebra is semisimple if and only if its Leibniz (co)homology with trivial coefficients vanishes. We also prove several results on the Lie and Leibniz cohomology ... More
Pirashvili's conjecture on the Leibniz homology for Lie algebrasAug 16 2019Sep 05 2019We prove a conjecture of Pirashvili, which says that a non-trivial finite-dimensional complex Lie algebra is semisimple if and only if its Leibniz (co)homology with trivial coefficients vanishes. We also prove several results on the Lie and Leibniz cohomology ... More
Sum-Essential Graphs of ModulesAug 16 2019The sum-essential graph $ \mathcal{S}_R(M) $ of a left $R$-module $M$ is a graph whose vertices are all nontrivial submodules of $M$ and two distinct submodules are adjacent iff their sum is an essential submodule of $M$. Properties of the graph $\mathcal{S}_R(M)$ ... More
The Injective Spectrum of a Right Noetherian Ring II: Sheaves and Torsion TheoriesAug 16 2019This is the second of two papers on the injective spectrum of a right noetherian ring. In the prequel, we considered the injective spectrum as a topological space associated to a ring (or, more generally, a Grothendieck category), which generalises the ... More
The Injective Spectrum of a Right Noetherian Ring I: Injective Spectra and Krull DimensionAug 16 2019The injective spectrum is a topological space associated to a ring $R$, which agrees with the Zariski spectrum when $R$ is commutative noetherian. We consider injective spectra of right noetherian rings (and locally noetherian Grothendieck categories) ... More
Holonomy Lie algebra of a fiber-type arrangementAug 16 2019We prove that the holonomy Lie algebra of a fiber-type arrangement is an iterated almost-direct product of a series of free Lie algebras with ranks the exponents of the arrangement. This is a Lie algebra version analogue of the well-known result of Falk-Randell ... More
Partial generalized crossed products and a seven-term exact sequenceAug 16 2019For a partial Galois extension of commutative rings we give a seven term exact sequence which generalize the Chase-Harrison-Rosenberg sequence.
Products of Ideals in Leavitt Path AlgebrasAug 16 2019Ideals in Leavitt path algebras have been shown to share many properties with those of integral domains. Since studying factorizations of ideals in integral domains into special types of ideals (particularly, prime, prime-power, primary, irreducible, ... More
Additive Local Multiplications and zero-preserving maps on $C(X)$Aug 15 2019Suppose $X$ is a compact Hausdorff space. In terms of topolocical properties of $X$, we find topological conditions on $X$ that are equivalent to each of the following: 1. every additive local multiplication on $C\left( X\right) $ is a multiplication, ... More
Actions of quantum linear spaces on quantum algebrasAug 14 2019We study actions of bosonizations of quantum linear spaces on quantum algebras. Under mild conditions, we classify actions on quantum affine spaces and quantum matrix algebras. In the former case, it is shown that all actions of generalized Taft algebras ... More
Quadratic Split Quaternion Polynomials: Factorization and GeometryAug 14 2019We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split quaternions.
On almost subnormal subgroups in division ringsAug 14 2019Let $D$ be a division ring with infinite center $F$, and $G$ an almost subnormal subgroup of $D^*$. In this paper, we show that if $G$ is locally solvable, then $G\subseteq F$. Also, assume that $M$ is a maximal subgroup of $G$. It is shown that if $M$ ... More
Actions of Small Groups on Two-Dimensional Artin-Schelter Regular AlgebrasAug 14 2019In commutative invariant theory, a classical result due to Auslander says that if $R = \Bbbk[x_1, \dots, x_n]$ and $G$ is a finite subgroup of $\text{Aut}_{\text{gr}}(R) \cong \text{GL}(n,\Bbbk)$ which contains no reflections, then there is a natural ... More
Computation of point modules of finitely semi-graded ringsAug 13 2019In this paper we compute the set of point modules of finitely semi-graded rings. In particular, from the parametrization of the point modules for the quantum affine n-space, the set of point modules for some important examples of non $\mathbb{N}$-graded ... More
Some open problems in the context of skew PBW extensions and semi-graded ringsAug 13 2019In this paper we discuss some open problems of non-commutative algebra and non-commutative algebraic geometry from the approach of skew $PBW$ extensions and semi-graded rings. More exactly, we will analyze the isomorphism arising in the investigation ... More
Some open problems in the context of skew PBW extensions and semi-graded ringsAug 13 2019Sep 18 2019In this paper we discuss some open problems of non-commutative algebra and non-commutative algebraic geometry from the approach of skew $PBW$ extensions and semi-graded rings. More exactly, we will analyze the isomorphism arising in the investigation ... More
Semigroup Models for Biochemical Reaction NetworksAug 13 2019The CRS (chemical reaction system) formalism by Hordijk and Steel is a versatile method to model self-sustaining biochemical reaction networks. Its distinguishing feature is the explicit assignment of catalytic function to chemicals that are part of the ... More
The automorphism group of the zero-divisor digraph of matrices over an antiringAug 13 2019We determine the automorphism group of the zero-divisor digraph of the semiring of matrices over an antinegative commutative semiring with a finite number of zero-divisors.
Homological properties of parafree Lie algebrasAug 13 2019In this paper, an explicit construction of a countable parafree Lie algebra over $\mathbb Z/2$ with nonzero second homology is given. It is also shown that the cohomological dimension of the pronilpotent completion of a free noncyclic finitely generated ... More
Reduction of matrices over simple Ore domainsAug 13 2019We study the theory of diagonal reductions of matrices over simple Ore domains of finite stable range. We cover the cases of 2-simple rings of stable range 1, Ore domains and certain cases of Bezout domains.