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We deal with the finite-dimensional mesh algebras given by stable translation quivers. These algebras are self-injective, and thus the stable categories have a structure of triangulated categories. Our main result determines the…

Representation Theory · Mathematics 2018-06-07 Sota Asai

In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which…

Rings and Algebras · Mathematics 2007-05-23 L. A. Simonian

In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of…

Representation Theory · Mathematics 2011-02-08 Ibrahim Assem , Diane Castonguay , Marcelo Lanzilotta , Rossana Vargas

We contribute to the classification of finite dimensional algebras under stable equivalence of Morita type. More precisely we give a classification of the class of Erdmann's algebras of dihedral, semi-dihedral and quaternion type and obtain…

Representation Theory · Mathematics 2010-05-20 Guodong Zhou , Alexander Zimmermann

The aim of this article is to study the Auslander algebra of any representation-finite string algebra. More precisely, we introduce the notion of gluing algebras and show that the Auslander algebra of a representation-finite string algebra…

Representation Theory · Mathematics 2024-10-16 Hui Chen , Jian He , Yu-Zhe Liu

We introduce quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The main result is a uniform formula describing the Ringel duals of these quasi-hereditary…

Representation Theory · Mathematics 2018-05-07 Martin Kalck , Joseph Karmazyn

Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations over an algebra. Such an existence occurs when an algebra is non-domestic; a conjecture due to M. Prest. G.…

Representation Theory · Mathematics 2026-03-05 Shantanu Sardar

Let A be a connected hereditary artin algebra. We show that the set of functorially finite torsion classes of A-modules is a lattice if and only if A is either representation-finite (thus a Dynkin algebra) or A has only two simple modules.…

Representation Theory · Mathematics 2014-02-07 Claus Michael Ringel

Let $A$ be a right noetherian algebra over a field $k$. If the base field extension $A \otimes_k K$ remains right noetherian for all extension fields $K$ of $k$, then $A$ is called stably right noetherian over $k$. We develop an inductive…

Rings and Algebras · Mathematics 2018-10-16 Daniel Rogalski

Let $k$ be an algebraically closed field. It is known that any stable equivalence between standard representation-finite self-injective $k$-algebras (without block of Loewy length 2) lifts to a standard derived equivalence, in particular,…

Representation Theory · Mathematics 2022-03-11 Nengqun Li , Yuming Liu

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

Rings and Algebras · Mathematics 2017-08-31 Miodrag Iovanov , Alexander Sistko

Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided…

Representation Theory · Mathematics 2024-04-12 I. Heckenberger , E. Meir , L. Vendramin

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

Quantum Algebra · Mathematics 2012-06-19 Hebing Rui

Using a new compactification of the (braid) configuration space of n points in the upper half plane we construct a family of exotic Lie-infinity automorphisms of the Schouten algebra of polyvector fields on an affine space depending on a…

Quantum Algebra · Mathematics 2010-11-15 S. A. Merkulov

We give a complete description of Lie algebras graded by an infinite irreducible locally finite root system.

Quantum Algebra · Mathematics 2011-06-28 Malihe Yousofzadeh

In an ongoing project to classify all hereditary abelian categories, we provide a classification of Ext-finite directed hereditary abelian categories satisfying Serre duality up to derived equivalence. In order to prove the classification,…

Category Theory · Mathematics 2007-05-23 Adam-Christiaan van Roosmalen

We give a complete description of the derived equivalence normal forms of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings. As a consequence, a description of the…

Representation Theory · Mathematics 2007-05-23 Rafal Bocian , Thorsten Holm , Andrzej Skowronski

A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_\Lambda$ and the inverse system algebra $R/I_\Delta$. We give a…

Commutative Algebra · Mathematics 2016-08-03 David Cook , Juan Migliore , Uwe Nagel , Fabrizio Zanello

We introduce the notion of a cellular system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for an algebra to be quasi-hereditary is the existence of a full divisible cellular…

Representation Theory · Mathematics 2007-05-23 Jie Du

Our first result provides a new characterization of Auslander algebras using a property of hereditary torsion pairs. The second result shows an Auslander algebra $\Lambda$ is left or right glued if and only if $\Lambda$ is…

Representation Theory · Mathematics 2021-07-07 Stephen Zito