Latest in math.ra

total 10801took 0.10s
Another approach to Hom-Lie bialgebras via Manin triplesMar 24 2019In this paper, we study Hom-Lie bialgebras by a new notion of the dual representation of a representation of a Hom-Lie algebra. Motivated by the essential connection between Lie bialgebras and Manin triples, we introduce the notion of a Hom-Lie bialgebra ... More
On the generalized distributive set of a finite nearfieldMar 22 2019For any nearfield $(R,+, \circ)$, denote by $D(R)$ the set of all distributive elements of $R$. Let $R$ be a finite Dickson nearfield that arises from Dickson pair $(q,n)$. For a given pair $(\alpha, \beta) \in R^2$ we study the generalized distributive ... More
The talented monoid of a Leavitt path algebraMar 22 2019There is a tight relation between the geometry of a directed graph and the algebraic structure of a Leavitt path algebra associated to it. In this note, we show a similar connection between the geometry of the graph and the structure of a certain monoid ... More
On the graded algebras associated with Hecke symmetries, II. The Hilbert seriesMar 21 2019This paper continues the work which attempts to understand the general properties of the graded algebras associated with Hecke symmetries without a restriction on the parameter q of the Hecke relation imposed in earlier results.
Noncyclic Division Algebras over Fields of Brauer Dimension OneMar 21 2019Let $K$ be a complete discretely valued field of rank one, with residue field $\Q_p$. It is well known that period equals index in $\Br(K)$. We prove that when $p=2$ there exist noncyclic $K$-division algebras of every $2$-power degree divisible by four. ... More
Research topics in finite groups and vertex algebrasMar 21 2019We suggest a few projects for studying vertex algebras with emphasis on finite group viewpoints.
On the Lie algebra structure of $HH^1(A)$ of a finite-dimensional algebra $A$Mar 20 2019Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. The second main result shows that ... More
Monomial $G$-posets and their Lefschetz invariantsMar 20 2019Let $G$ be a finite group, and $C$ be an abelian group. We introduce the notions of $C$-monomial $G$-sets and $C$-monomial $G$-posets, and state some of their categorical properties. This gives in particular a new description of the $C$-monomial Burnside ... More
Some remarks on non projective Frobenius algebras and linear codesMar 20 2019With a small suitable modification, dropping the projectivity condition, we extend the notion of a Frobenius algebra to grant that a Frobenius algebra over a Frobenius commutative ring is itself a Frobenius ring. The modification introduced here also ... More
Castelnuovo-Mumford regularity of $\mathrm{FI}^m$-modules presented in finite degreesMar 20 2019Let $V$ be a representation of the category $\mathrm{FI}^m$, a product of $m$ copies of the category of finite sets and injections, over an arbitrary commutative coefficient ring. We show in this paper that $V$ has finite Castelnuovo-Mumford regularity ... More
Integral forms in vertex operator algebras, a surveyMar 20 2019We give a brief survey of recent work on integral forms in vertex operator algebras (VOAs).
Determinants for integral forms in lattice type vertex operator algebrasMar 19 2019We prove a determinant formula for the standard integral form of a lattice vertex operator algebra.
Coneat Injective ModulesMar 19 2019A module is called coneat injective if it is injective with respect to all coneat exact sequences. The class of such modues is enveloping and falls properly between injectives and pure injectives. Generalizations of coneat injectivity, like relative coneat ... More
Frobenius bimodules and flat-dominant dimensionsMar 19 2019We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules. This is motivated by the Nakayama conjecture and an approach of Martinez-Villa to the Auslander-Reiten conjecture on stable ... More
Generators for Coulomb branches of quiver gauge theoriesMar 18 2019We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings. We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch, once the deformation ... More
On commutative differential graded algebrasMar 18 2019In this paper we undertake a basic study on connective commutative differential graded algebras (CDGA), more precisely, piecewise Noetherian CDGA, which is a DG-counter part of commutative Noetherian algebra. We establish basic results for example, Auslaner-Buchsbaum ... More
Mixed Witt rings of algebras with involution of the first kindMar 18 2019The Witt ring $W(K)$ of a field is a central object in the algebraic theory of quadratic forms. In general, we can define a Witt ring for commutative rings with involution. But if $(A,\sigma)$ is a central simple algebra with involution of the first over ... More
Multiplayer Rock-Paper-ScissorsMar 18 2019We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by (hyper)tournament algebras, count these algebras, study their automorphisms, ... More
Derivations and deformations of $δ$-Jordan Lie supertriple systemsMar 18 2019Let $T$ be a $\delta$-Jordan Lie supertriple system. We first introduce the notions of generalized derivations and representations of $T$ and present some properties. Also, we study the low dimension cohomology and the coboundary operator of $T$, and ... More
Orbit equivalence of higher-rank graphsMar 17 2019We study the notions of continuous orbit equivalence and eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs with finitely many vertices and no sinks or sources. We show that there ... More
Relative $B$-groupsMar 17 2019This paper extends the notion of $B$-group to a relative context. For a finite group $K$ and a field $\mathbb{F}$ of characteristic 0, the lattice of ideals of the Green biset functor $\mathbb{F}B_K$ obtained by shifting the Burnside functor $\mathbb{F}B$ ... More
Quadratic differential algebras generated by Euclidean spacesMar 17 2019We define a class of quadratic differential algebras which are generated as differential graded algebras by the elements of an Euclidean space. Such a differential algebra is a differential calculus over the quadratic algebra of its elements of differential ... More
The isomorphism problem for universal enveloping algebras of four-dimensional solvable Lie algebrasMar 16 2019This paper is a contribution to the isomorphism problem for universal enveloping algebras of finite-dimensional Lie algebras. The main result is that this problem has a positive solution in the class of solvable Lie algebras of dimension at most four ... More
max-projective modulesMar 14 2019A right $R$-module $M$ is called max-projective provided that each homomorphism $f:M \to R/I$ where $I$ is any maximal right ideal, factors through the canonical projection $\pi : R \to R/I$. We call a ring $R$ right almost-$QF$ (resp. right max-$QF$) ... More
$n$-dervations of Lie color algebrasMar 14 2019The aim of this article is to discuss the $n$-derivation algebras of Lie color algebras. It is proved that, if the base ring contains $\frac{1}{n-1}$, $L$ is a perfect Lie color algebra with zero center, then every triple derivation of $L$ is a derivation, ... More
Gabriel-Roiter measure, representation dimension and rejective chainsMar 13 2019The Gabriel-Roiter measure is used to give an alternative proof of the finiteness of the representation dimension for Artin algebras, a result established by Iyama in 2002. The concept of Gabriel-Roiter measure can be extended to abelian length categories ... More
Pseudo effect algebras as algebras over bounded posetsMar 13 2019We prove that there is a monadic adjunction between the category of bounded posets and the category of pseudo effect algebras.
Multiplicative derivations on rank-$s$ matrices for relatively small $s$Mar 12 2019Let $n$ and $s$ be fixed integers such that $n\geq 2$ and $1\leq s\leq \frac{n}{2}$. Let $M_n(\mathbb{K})$ be the ring of all $n\times n$ matrices over a field $\mathbb{K}$. If a map $\delta:M_n(\mathbb{K})\rightarrow M_n(\mathbb{K})$ satisfies that $\delta(xy)=\delta(x)y+x\delta(y)$ ... More
Recursive Matrix Algorithms in Commutative Domain for Cluster with Distributed MemoryMar 11 2019We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parallel programs based on these algorithms on a supercomputer MVS-10P at the ... More
Affine and Projective Planes Linked with Projective Lines over Certain Rings of Lower Triangular MatricesMar 11 2019Mar 13 2019Let $T_n(q)$ be the ring of lower triangular matrices of order $n \geq 2$ with entries from the finite field $F(q)$ of order $q \geq 2$ and let ${^2T_n(q)}$ denote its free left module. For $n=2,3$ it is shown that the projective line over $T_n(q)$ gives ... More
Affine and Projective Planes Linked with Projective Lines over Certain Rings of Lower Triangular MatricesMar 11 2019Let $T_n(q)$ be the ring of lower triangular matrices of order $n \geq 2$ with entries from the finite field $F(q)$ of order $q \geq 2$ and let ${^2T_n(q)}$ denote its free left module. For $n=2,3$ it is shown that the projective line over $T_n(q)$ gives ... More
On free subsemigroups of associative algebrasMar 11 2019Mar 12 2019In 1992, following earlier conjectures of Lichtman and Makar-Limanov, Klein conjectured that a noncommutative domain must contain a free multiplicative noncyclic subsemigroup. He verfied the conjecture when the center is uncountable. In this note, we ... More
On free subsemigroups of associative algebrasMar 11 2019In 1992, following earlier conjectures of Lichtman and Makar-Limanov, Klein conjectured that a noncommutative domain must contain a free multiplicative noncyclic subsemigroup. He verfied the conjecture when the center is uncountable. In this note, we ... More
Cup-product for Hom-Leibniz cohomologyMar 10 2019We define a cup-product for Hom-Leibniz cohomology and show that the cup-product satisfies a graded Hom-zinbiel type relation.
BiHom-pre-alternative algebras and BiHom-alternative quadri-algebrasMar 10 2019The purpose of this paper is to introduce and study the notion of BiHom-pre-alternative algebra which may be viewed as a BiHom-alternative algebra whose product can be decomposed into two compatible pieces. Furthermore, we introduce the notion of BiHom-alternative ... More
Abelian Endoregular ModulesMar 09 2019In this paper, we introduce the notion of abelian endoregular modules as those modules whose endomorphism rings are abelian von Neumann regular. We characterize an abelian endoregular module $M$ in terms of its $M$-generated submodules. We prove that ... More
Upper Characteristic Trees of a Lie AlgebraMar 09 2019In this paper, we introduce upper characteristic trees for finite dimensional Lie algebras. The ideals of a finite dimensional Lie algebra are distributed as nodes of some upper characteristic trees. A node is connected with an upper level node in an ... More
Extensions of $\frak{sl}_2$ by generalized derivations and Hom-Lie algebra structures on simple Lie algebrasMar 08 2019The purpose of this paper is to show that there are Hom-Lie algebras structures on $\mathfrak{sl}_2(\mathbb{F}) \oplus \mathbb{F}D$, where $D$ is an special type of generalized derivation of $\mathfrak{sl}_2(\mathbb{F})$, and $\mathbb{F}$ is an algebraically ... More
Extensions of $\frak{sl}_2$ by generalized derivations and Hom-Lie algebra structures on simple Lie algebrasMar 08 2019Mar 13 2019The purpose of this paper is to show that there are Hom-Lie algebra structures on $\mathfrak{sl}_2(\mathbb{F}) \oplus \mathbb{F}D$, where $D$ is a special type of generalized derivation of $\mathfrak{sl}_2(\mathbb{F})$, and $\mathbb{F}$ is an algebraically ... More
On Lenagan's Theorem for finite length bimodulesMar 08 2019We offer a self-contained proof of Lenagan's Theorem which does not rely on Goldie's Theorem
Left saturation closure for Ore localizationsMar 07 2019In this paper, we introduce the notion of LSat, the left saturation closure of a subset of a module at a subset of the base ring, which generalizes multiple important concepts related to Ore localization. We show its significance in finding a saturated ... More
Generalized Igusa functions and ideal growth in nilpotent Lie ringsMar 07 2019We introduce a new class of combinatorially defined rational functions and apply them to deduce explicit formulae for local ideal zeta functions associated to the members of a large class of nilpotent Lie rings which contains the free class-2-nilpotent ... More
Fixed rings in quotients of completed group ringsMar 07 2019Let $k$ be $\mathbb{F}_p$ or $\mathbb{Z}_p$, let $G$ be a compact $p$-adic analytic group, and form its completed group algebra $kG$. Take a closed subgroup $\Gamma$ of $G$. We analyse the structure of the fixed ring of $kG/I$ under the conjugation action ... More
Restricted shifted Yangians and restricted finite $W$-algebrasMar 07 2019We study the truncated shifted Yangian $Y_{n,l}(\sigma)$ over an algebraically closed field $\mathbb{k}$ of characteristic $p > 0$, which is known to be isomorphic to the finite $W$-algebra $U(\mathfrak{g}, e)$ associated to a corresponding nilpotent ... More
Almost zip Bezout domainMar 07 2019J. Zelmanowitz introduced the concept of ring, which we call zip rings. In this paper we characterize a commutative Bezout domain whose finite homomorphic images are zip rings modulo its nilradical.
Poincare-Birkhoff-Witt theorem for pre-Lie and postLie algebrasMar 06 2019We construct the universal enveloping preassociative and postassociative algebra for a pre-Lie and a postLie algebra respectively. We show that the pairs $(\mathrm{preLie},\mathrm{preAs})$ and $(\mathrm{postLie},\mathrm{postAs})$ are Poincare-Birkhoff-Witt-pairs, ... More
Nil Clean Divisor GraphMar 06 2019In this article, we introduce a new graph theoretic structure associated with a finite commutative ring, called nil clean divisor graph. For a ring $R$, nil clean divisor graph is denoted by $G_N(R)$, where the vertex set is $\{x\in R\,:\, x\neq 0, \,\exists\, ... More
The structures of Hopf $\ast$-algebra on Radford algebrasMar 06 2019We investigate the structures of Hopf $\ast$-algebra on the Radford algebras over $\mathbb {C}$. All the $*$-structures on $H$ are explicitly given. Moreover, these Hopf $*$-algebra structures are classified up to equivalence.
Unified products of Leibniz conformal algebrasMar 06 2019The aim of this paper is to provide an answer to the $\mathbb{C}[\partial]$-split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on $E=R\oplus Q$ up to an isomorphism ... More
Gelfand--Dorfman algebras, derived identities, and the Manin product of operadsMar 06 2019Gelfand--Dorfman bialgebras (GD-algebras) are nonassociative systems with two bilinear operations satisfying a series of identities that express Hamiltonian property of an operator in the formal calculus of variations. The paper is devoted to the study ... More
Cohomologies of a Lie algebra with a derivation and applicationsMar 06 2019The main object of study of this paper is the notion of a LieDer pair, i.e. a Lie algebra with a derivation. We introduce the concept of a representation of a LieDer pair and study the corresponding cohomologies. We show that a LieDer pair is rigid if ... More
Maps between rectangular matrix spaces preserving disjointness, (zero) triple product or normsMar 05 2019Let $M_{m,n}$ be the set of $m\times n$ real or complex rectangular matrices. Two matrices $A, B \in M_{m,n}$ are disjoint if $A^*B = 0_n$ and $AB^* = 0_m$. In this paper, characterization is given for linear maps $\Phi: M_{m,n} \rightarrow M_{r,s}$ sending ... More
Maximal orthogonal sets of unimodular vectors over finite local rings of odd characteristicMar 05 2019Let $R$ be a finite local ring of odd characteristic and $\beta$ a non-degenerate symmetric bilinear form on $R^2$. In this short note, we determine the largest possible cardinality of pairwise orthogonal sets of unimodular vectors in $R^2$.
Morita theory of systemsMar 05 2019We present the rudiments of the Morita theory of module systems (over semirings), paralleling the classical Morita theory over associative rings.
Tensor product of correspondence functorsMar 05 2019As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra ... More
A complete classification of three-dimensional algebras over ${\mathbb R}$ and ${\mathbb C}$Mar 05 2019We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a complete elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We compare our results ... More
Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebraMar 04 2019For each nonzero $h\in \mathbb{F}[x]$, where $\mathbb{F}$ is a field, let $\mathsf{A}_h$ be the unital associative algebra generated by elements $x,y$, satisfying the relation $yx-xy = h$. This gives a parametric family of subalgebras of the Weyl algebra ... More
Quantum cluster algebras via Hall algebras of morphismsMar 03 2019We realize the quantum cluster algebra with principal coefficients as a subquotient of certain Hall algebra involving the category of morphisms between projectives.
Enumeration and Asymptotic Formulas for Rectangular Partitions of the HypercubeMar 03 2019We study a two-parameter generalization of the Catalan numbers: $C_{d,p}(n)$ is the number of ways to subdivide the $d$-dimensional hypercube into $n$ rectangular blocks using orthogonal partitions of fixed arity $p$. Bremner \& Dotsenko introduced $C_{d,p}(n)$ ... More
Irreducible representation-types of Leavitt path algebrasMar 02 2019Irreducible representations of both Leavitt and Cohn path algebras of an arbitrary digraph with coefficients in a commutative field is classified. They are constructed in several ways using both infinite paths on the right as well as direct limits or ... More
Irreducible representation-types of Leavitt path algebrasMar 02 2019Mar 22 2019Irreducible representations of both Leavitt and Cohn path algebras of an arbitrary digraph with coefficients in a commutative field is classified. They are constructed in several ways using both infinite paths on the right as well as direct limits or ... More
Gravity algebra structure on the negative cyclic homology of Calabi-Yau algebrasMar 02 2019Mar 12 2019In this paper, we study the Lie$_\infty$ (also called gravity) algebra structure on the negative cyclic homology or the cyclic cohomology of several classes of algebras. These algebras include: Calabi-Yau algebras, symmetric Frobenius algebras, unimodular ... More
Koszul duality and the Hochschild cohomology of Artin-Schelter regular algebrasMar 02 2019We identify two Batalin-Vilkovisky algebra structures, one obtained by Kowalzig and Krahmer on the Hochschild cohomology of an Artin-Schelter regular algebra with semisimple Nakayama automorphism and the other obtained by Lambre, Zhou and Zimmermann on ... More
Local superderivations on Cartan type Lie superalgebrasMar 02 2019In this paper, we characterize the local superderivations on Cartan type Lie superalgebras over the complex field $\mathbb{C}$. Furthermore, we prove that every local superderivations on Cartan type simple Lie superalgebras is a superderivations. As an ... More
On basic and Bass quaternion ordersMar 01 2019A quaternion order O over a Dedekind domain R is Bass if every R-superorder is Gorenstein, and O is basic if it contains an integrally closed quadratic R-order. In this article, we show that these conditions are equivalent in local and global settings: ... More
On universal modules with pure embeddingsMar 01 2019Mar 12 2019We show that certain classes of modules have universal models with respect to pure embeddings. $Theorem.$ Let $R$ be a ring, $T$ a first-order theory with an infinite model extending the theory of $R$-modules and $K^T=(Mod(T), \leq_{pp})$ (where $\leq_{pp}$ ... More
On universal modules with pure embeddingsMar 01 2019We show that certain classes of modules have universal models with respect to pure embeddings. $Theorem.$ Let $R$ be a ring, $T$ a first-order theory with an infinite model extending the theory of $R$-modules and $K^T=(Mod(T), \leq_{pp})$ (where $\leq_{pp}$ ... More
Commutative Post-Lie algebra structures on nilpotent Lie algebras and Poisson algebrasMar 01 2019We give an explicit description of commutative post-Lie algebra structures on some classes of nilpotent Lie algebras. For non-metabelian filiform nilpotent Lie algebras and Lie algebras of strictly upper-triangular matrices we show that all CPA-structures ... More
Classical simple Lie 2-algebras of toral rank 3 and a contragredient Lie 2-algebra of toral rank 4Feb 28 2019In this paper we show there are no classical type simple Lie 2-algebras with toral rank odd and we also show that the simple contragredient Lie 2-algebra $G(F_{4, a})$ of dimension 34 has toral rank 4, and we give the Cartan decomposition of $G(F_{4, ... More
On simple Lie 2-algebra of toral rank 3Feb 28 2019Simple Lie algebras of finite dimension over an algebraically closed field of characteristic 0 or $p> 3$ were recently classified. However, the problem over an algebraically closed field of characteristics 2 or 3 there exist only partial results. The ... More
The central nilradical of nonnoetherian dimer algebrasFeb 28 2019Let $Z$ be the center of a nonnoetherian dimer algebra on a torus. We show that the nilradical $\operatorname{nil}Z$ of $Z$ is prime, may be nonzero, and consists precisely of the central elements that vanish under a cyclic contraction. This implies that ... More
Tensor product of dimension effect algebrasFeb 28 2019Dimension effect algebras were introduced in (A. Jencova, S. Pulmannova, Rep. Math. Phys. 62 (2008), 205-218), and it was proved that they are unit intervals in dimension groups. We prove that the effect algebra tensor product of dimension effect algebras ... More
A generalisation of Dickson's commutative division algebrasFeb 28 2019Dickson's commutative semifields are an important class of finite division algebras. We generalise Dickson's construction of commutative division algebras by doubling both finite field extensions and central simple algebras and not restricting us to the ... More
A central idempotent in the endomorphism algebra of a finite latticeFeb 27 2019We give a direct construction of a specific idempotent in the endomorphism algebra of a finite lattice $T$. This idempotent is associated with all possible sublattices of $T$ which are total orders.
An exponential lower bound for the degrees of invariants of cubic forms and tensor actionsFeb 27 2019Using the Grosshans Principle, we develop a method for proving lower bounds for the maximal degree of a system of generators of an invariant ring. This method also gives lower bounds for the maximal degree of a set of invariants that define Hilbert's ... More
Skew-constacyclic codes over $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$Feb 27 2019In this paper, the investigation on the algebraic structure of the ring $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$ and the description of its automorphism group, enable to study the algebraic structure of codes and their dual over this ring. We ... More
Pseudo BCI-algebras with derivationsFeb 26 2019In this paper we define two types of implicative derivations on pseudo-BCI algebras, we investigate their properties and we give a characterization of regular implicative derivations of type II. We also define the notion of a d-invariant deductive system ... More
Normal group algebrasFeb 25 2019Let $\mathbb{F}G$ denote the group algebra of the group $G$ over the field $\mathbb{F}$ with $char(\mathbb{F})\neq 2$. Given both a homomorphism $\sigma:G\rightarrow \{\pm1\}$ and a group involution $\ast: G\rightarrow G$, an oriented involution of $\mathbb{F}G$ ... More
Darboux-Jouanolou Integrability for Arbitrary FieldsFeb 25 2019We prove a Darboux-Jouanolou type theorem on the algebraic integrability of differential 1-forms over arbitrary fields.
Darboux-Jouanolou Integrability for Arbitrary FieldsFeb 25 2019Mar 11 2019We prove a Darboux-Jouanolou type theorem on the algebraic integrability of differential 1-forms over arbitrary fields.
Bases for upper cluster algebras and tropical pointsFeb 25 2019It is known that many (upper) cluster algebras possess different kinds of good bases which contain the cluster monomials and are parametrized by the tropical points of cluster Poisson varieties. For injective reachable upper cluster algebras, we describe ... More
Cohen-Macaulay modules over Yoneda algebrasFeb 25 2019For a finite dimensional algebra $\Lambda$ of finite representation type and an additive generator $M$ for $\mathrm{mod}\,\Lambda$, we investigate the properties of the Yoneda algebra $\Gamma=\bigoplus_{i \geq 0}\mathrm{Ext}_\Lambda^i(M,M)$. We show that ... More
Centrosymmetric nonnegative realization of spectraFeb 25 2019A list $\Lambda =\{\lambda _{1},\lambda _{2},\ldots ,\lambda _{n}\}$ of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. In this paper we intent to characterize those lists of complex numbers, which are ... More
$F$-matrices of cluster algebras from triangulated surfacesFeb 25 2019For a given marked surface $(S,M)$ and a fixed tagged triangulation $T$ of $(S,M)$, we show that each tagged triangulation $T'$ of $(S,M)$ is uniquely determined by the intersection numbers of tagged arcs of $T$ and tagged arcs of $T'$. As an application, ... More
$F$-matrices of cluster algebras from triangulated surfacesFeb 25 2019Mar 12 2019For a given marked surface $(S,M)$ and a fixed tagged triangulation $T$ of $(S,M)$, we show that each tagged triangulation $T'$ of $(S,M)$ is uniquely determined by the intersection numbers of tagged arcs of $T$ and tagged arcs of $T'$. As an application, ... More
A note on solution of $ax+xb=c$ by Clifford algebrasFeb 25 2019The coordinate-free solutions of the multivector equation $ax+xb=c$ are discussed and presented for the Clifford algebras $Cl_{p,q}$ when $p+q\le 3$.
The Extension Dimension of Abelian CategoriesFeb 25 2019Let $\A$ be an abelian category having enough projective objects and enough injective objects. We prove that if $\A$ admits an additive generating object, then the extension dimension and the weak resolution dimension of $\A$ are identical, and they are ... More
Simplicial complexes and tilting theory for Brauer tree algebrasFeb 23 2019We study 2-term tilting complexes of Brauer tree algebras in terms of simplicial complexes. We show the symmetry and convexity of the simplicial complexes as lattice polytopes. Via a geometric interpretation of derived equivalences, we show that the $f$-vector ... More
Graded change of ringFeb 22 2019We investigate scalar restriction, scalar extension, and scalar coextension functors for graded modules, including their interplay with coarsening functors, graded tensor products, and graded Hom functors. This leads to several characterisations of epimorphisms ... More
On 3-dimensional complex Hom-Lie algebrasFeb 22 2019In this paper, we study and classify the 3-dimensional Hom-Lie algebras over C. We provide first a complete set of representatives for the isomorphism classes of skew-symmetric bilinear products defined on a 3-dimensional complex vector space g. The well ... More
On 3-dimensional complex Hom-Lie algebrasFeb 22 2019Feb 26 2019In this paper, we study and classify the 3-dimensional Hom-Lie algebras over C. We provide first a complete set of representatives for the isomorphism classes of skew-symmetric bilinear products defined on a 3-dimensional complex vector space g. The well ... More
Upper bounds for the length of non-associative algebrasFeb 22 2019We obtain a sharp upper bound for the length of arbitrary non-associative algebra and present an example demonstrating the sharpness of our bound. To show this we introduce a new method of characteristic sequences based on linear algebra technique. This ... More
The harmonicity of slice regular functionsFeb 21 2019In this article we investigate harmonicity, Laplacians, mean value theorems and related topics in the context of quaternionic analysis. We start by improving the definition of slice regular function over the quaternions $\mathbb{H}$ given by Gentili-Struppa ... More
On the image of polynomials evaluated on incidence algebras: a counter-example and a solutionFeb 21 2019In this paper, we investigate the subset obtained by evaluations of a fixed multilinear polynomial on a given algebra. We provide an example of a multilinear polynomial, whose image is not a vector subspace; namely, the product of two commutators need ... More
Characteristic free description of semi-invariants of $2\times 2$ matricesFeb 21 2019A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given. In an alternative interpretation this yields a minimal system ... More
Higher preprojective algebras, Koszul algebras, and superpotentialsFeb 21 2019Feb 22 2019In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting. We first show that the quiver of the higher preprojective algebra is obtained by adding arrows ... More
Higher preprojective algebras, Koszul algebras, and superpotentialsFeb 21 2019In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting. We first show that the quiver of the higher preprojective algebra is obtained by adding arrows ... More
On the minimal number of generators of an étale algebraFeb 20 2019O. Forster proved that over a ring R of Krull dimension d a finite module M of rank at most n can be generated by n + d elements. Generalizing this in great measure U. First and Z. Reichstein showed that any finite R-algebra A can be generated by n + ... More
Representations and cohomologies of Hom-pre-Lie algebrasFeb 20 2019In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of Hom-pre-Lie algebras in term of the cohomology theory of Hom-Lie algebras. As applications, we study linear ... More
On the spectral properties of real anti-tridiagonal Hankel matricesFeb 19 2019In this paper we express the eigenvalues of real anti-tridiagonal Hankel matrices as the zeros of given rational functions. We still derive eigenvectors for these structured matrices at the expense of prescribed eigenvalues.