Related papers: Classification of modules over laterally complete …

Let $\Lambda$ be an $n$-Auslander algebra with global dimension $n+1$. In this paper, we prove that $\Lambda$ is representation-finite if and only if the number of non-isomorphic indecomposable $\Lambda$-modules with projective dimension…

Let $\Gamma^+$ be the positive cone in a totally ordered abelian group $\Gamma$, and let $\alpha$ be an action of $\Gamma^+$ by endomorphisms of a $C^*$-algebra $A$. We consider a new kind of crossed-product $C^*$-algebra…

A graph $\Gamma$ is $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of arcs of $\Gamma$, where an arc is an ordered pair of adjacent vertices. Let $\Gamma$ be a $G$-symmetric graph such that its…

Let $A$ be an $n$-dimensional algebra over a field $k$ and $a(A)$ its quantum symmetry semigroup. We prove that the automorphisms group ${\rm Aut}_{\rm Alg} (A)$ of $A$ is isomorphic to the group $U \bigl( G(a (A)^{\rm o} ) \bigl)$ of all…

We exhibit an isomorphism of associative algebras between the $\operatorname{Ext}$-algebra $\operatorname{Ext}_\Lambda^\ast(\Delta,\Delta)$ of standard modules over the dual extension algebra $\Lambda$ of two directed algebras $B$ and $A$…

Let $\Gamma=\Gamma(A)$ denote a simple strongly connected digraph with vertex set $X$, diameter $D$, and let $\{A_0,A:=A_1,A_2,\ldots,A_D\}$ denote the set of distance-$i$ matrices of $\Gamma$. Let $\{R_i\}_{i=0}^D$ denote a partition of…

We study in this article the dual of a (strictly) commutative group stack $G$ and give some applications. Using the Picard functor and the Picard stack of $G$, we first give some sufficient conditions for $G$ to be dualizable. Then, for an…

An R-algebra A is called E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra End_RA of the R-module {}_R A, taking any a in A to the right multiplication a_r in End_R A by a is an isomorphism of algebras. In this…

Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.

A graph $\Gamma$ is a bi-Cayley graph over a group $G$ if $G$ is a semiregular group of automorphisms of $\Gamma$ having two orbits. Let $G$ be a non-abelian metacyclic $p$-group for an odd prime $p$, and let $\Gamma$ be a connected…

Let $\Lambda,\Gamma$ be rings and $R=\left(\begin{array}{cc}\Lambda & 0 \\ M & \Gamma\end{array}\right)$ the triangular matrix ring with $M$ a $(\Gamma,\Lambda)$-bimodule. Let $X$ be a right $\Lambda$-module and $Y$ a right $\Gamma$-module.…

A graph $\Gamma$ is called $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of $G$-symmetric graphs $\Gamma$ with $V(\Gamma)$ admitting…

For a commutative ring $A$, we have the category of (bounded-below) chain complexes of $A$-modules $Ch_{+}(A\mymod)$, a closed symmetric monoidal category with a compatible stable Quillen model structure. The associated homotopy category is…

A graph Gamma is said to be 2-arc-transitive if its full automorphism group Aut(\Gamma) has a single orbit on ordered paths of length 2, and for G\leq Aut(\Gamma), \Gamma is G-regular if G is regular on the vertex set of \Gamma. Let G be a…

Let A and B be finite dimensional simple real algebras with division gradings by an abelian group G. In this paper we give necessary and sufficient conditions for the coincidence of the graded identities of A and B. We also prove that every…

This paper deals with the variety of commutative nonassociative algebras satisfying the identity $L_x^3+ \gamma L_{x^3} = 0$, $\gamma \in K$. Correa et al proved that if $\gamma = 0,1$ then any such finitely generated algebra is nilpotent.…

For a congruence subgroup $\Gamma$, we define the notion of $\Gamma$-equivalence on binary quadratic forms which is the same as proper equivalence if $\Gamma = \mathrm{SL}_2(\mathbb Z)$. We develop a theory on $\Gamma$-equivalence such as…

The commutative differential graded algebra $A_{\mathrm{PL}}(X)$ of polynomial forms on a simplicial set $X$ is a crucial tool in rational homotopy theory. In this note, we construct an integral version $A^{\mathcal{I}}(X)$ of…

Using the computational algebra system GAP (http://www.gap-system.org) and the GAP package LAGUNA (http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm), we checked that all 2-groups of order not greater than 32 are determined by normalized…

For a group $G$ and a subset $X$ of $G$, the commuting graph of $X$, denoted by $\Gamma(G,X)$ is the graph whose vertex set is $X$ and any two vertices $u$ and $v$ in $X$ are adjacent if and only if they commute in $G$. In this article,…