Related papers: AR-components for generalized Beilinson algebras

We determine the length of composition series of projective modules of G-transitive algebras with an Auslander-Reiten component of Euclidean tree class. Furthermore we show that modules with certain length of composition series are…

In this paper we establish the generalized Beukers integral $I_{m}(a_{1},...,a_{n})$ with some methods of partial fraction decomposition. Thus one obtains an explicit expression of the generalized Beukers integral. Further, we estimate the…

We characterize the generalized Auslander--Reiten duality on the category of finitely presented modules over some certain Hom-finite category. Examples include the category FI of finite sets with injections, and the one VI of finite…

Following the work of Beilinson-Bernstein and Kashiwara-Rouquier, we give a geometric interpretation of certain categories of modules over the finite W-algebra. As an application we reprove the Skryabin equivalence.

Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ and then…

Let $Q$ be the 3-Kronecker quiver, i.e., $Q$ has two vertices, labeled by 1 and 2, and three arrows from 2 to 1. Fix an algebraically closed field $k$. Let $\mathcal{C}$ be a regular component of the Auslander-Reiten quiver containing an…

We deduce factorization properties for a quasi-Banach module over a quasi-Banach algebra. Especially we extend a result by Hewitt and prove that if any such algebra which possess a bounded left approximate identity, then any element in the…

Generalized Weyl Algebras (GWAs) appear in diverse areas of mathematics including mathematical physics, noncommutative algebra, and representation theory. We study the invariants of quantum GWAs under finite automorphisms. We extend a…

Let $\tau$ be a strongly $(n,p;a,c)$ regular graph,such that $0<c<p<n-1,$ $A$ his matrix of adjacency and let ${\cal V}_{n}$ be the Euclidean space spanned by the powers of $A$ over the reals where the scallar product $\bullet|\bullet$ is…

Let $\mathbb{K}$ denote an algebraically closed field and $A$ a free product of finitely many semisimple associative $\mathbb{K}$-algebras. We associate to $A$ a finite acyclic quiver $\Gamma$ and show that the category of finite…

We say a group $G$ has property $R_\infty$ if the number $R(\varphi)$ of twisted conjugacy classes is infinite for every automorphism $\varphi$ of $G$. For such groups, the $R_\infty$-nilpotency degree is the least integer $c$ such that…

For a split reductive algebraic group, this paper observes a homological interpretation for Weyl module multiplicities in Jantzen's sum formula. This interpretation involves an Euler characteristic built from Ext groups between integral…

Given an odd prime $p$, we investigate the position of simple modules in the stable Auslander-Reiten quiver of the principal block of a finite group with non-cyclic abelian Sylow $p$-subgroups. In particular, we prove a reduction to finite…

Let $G=GL(m|n)$ be a general linear supergroup over an algebraically closed field $k$ of odd characteristic $p$. In this paper we construct Jantzen filtration of Weyl modules $V(\lambda)$ of $G$ when $\lambda$ is a typical weight in the…

We consider the homotopy category of perfect complexes for a finite dimensional self-injective algebra over a field, identifying many aspects of perfect complexes according to their position in the Auslander-Reiten quiver. Short complexes…

We prove a localization theorem for affine $W$-algebras in the spirit of Beilinson--Bernstein and Kashiwara--Tanisaki. More precisely, for any non-critical regular weight $\lambda$, we identify $\lambda$-monodromic Whittaker $D$-modules on…

We study Artin algebras $A$ and commutative Noetherian complete local rings $R$ in connection with the following decomposition property of Gorenstein-projective modules: $(*)$ any Gorenstein-projective module is a direct sum of finitely…

We prove that over a commutative noetherian ring the three approaches to introducing depth for complexes: via Koszul homology, via Ext modules, and via local cohomology, all yield the same invariant. Using this result, we establish a far…

We use $t$-structures on the homotopy category $K^b(R-mod)$ for an artin algebra $R$ and Watts' representability theorem to give an existence proof for Auslander-Reiten sequences of $R$-modules.

Let $B$ be a generalized Koszul algebra over a finite dimensional algebra $S$. We construct a bimodule Koszul resolution of $B$ when the projective dimension of $S_B$ equals 2. Using this we prove a Poincar\'e-Birkhoff-Witt (PBW) type…