Hafezi, Rasool
Published in
Forum Mathematicum

In this paper we show that how the representation theory of subcategories (of the category of modules over an Artin algebra) can be connected to the representation theory of all modules over some algebra. The subcategories dealing with are some certain subcategories of the morphism categories (including submodule categories studied recently by Ring...

Enomoto, Masatoshi Watatani, Yasuo
Published in
Advances in Operator Theory

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded operators are determined by unitarily equivalent classes of the operator ranges and the nullity of the original bou...

Bissinger, Daniel
Published in
Forum Mathematicum

Inspired by recent work of Carlson, Friedlander and Pevtsova concerning modules for p-elementary abelian groups E r {E_{r}} of rank r over a field of characteristic p > 0 {p>0} , we introduce the notions of modules with constant d-radical rank and modules with constant d-socle rank for the generalized Kronecker algebra 𝒦 r = k Γ r {\mathcal{K}_{r...

Iovanov, Miodrag Cristian Sistko, Alexander Harris
Published in
Forum Mathematicum

We study maximal associative subalgebras of an arbitrary finite-dimensional associative algebra B over a field 𝕂 {\mathbb{K}} and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case and then lifting to non-semisimple algebras. The results are sharpest in t...

You, Hanyang Zhang, Pu
Published in
Frontiers of Mathematics in China

We classify all the indecomposable modules of dimension ⩽ 5 over the quantum exterior algebra k〈x, y〉/〈x2, y2, xy + qyx〉 in two variables, and all the indecomposable modules of dimension ⩽ 3 over the quantum complete intersection k〈x, y〉/〈xm, yn, xy + qyx〉 in two variables, where m or n ⩾ 3; by giving explicitly their diagram presentations.

Liu, Yu Zhe Zhang, Chao
Published in
Acta Mathematica Sinica, English Series

An algebra A is called derived-unique provided that any algebra which is derived equivalent to A is necessarily Morita equivalent to A. We classify derived-unique gentle algebras with at most one cycle using the combinatorial invariant introduced by Avella-Alaminos and Geiss.

Chaio, Claudia Le Meur, Patrick Trepode, Sonia
Published in
Algebras and Representation Theory

The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the module category. When the ground ring is a perfect field, and the given morphism behaves nicely with respect to co...

Andruskiewitsch, Nicolás Bagio, Dirceu Della Flora, Saradia Flôres, Daiana
Published in
São Paulo Journal of Mathematical Sciences

Let H and K be the bosonizations of the Jordan and super Jordan plane by the group algebra of a cyclic group; the algebra K projects onto an algebra L that can be thought of as the quantum Borel of sl(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{...

Guo, Junying Guo, Xiaojiang
Published in
Open Mathematics

Strict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In pa...

Yildirim, Emine
Published in
Algebras and Representation Theory

Let J(C) be the poset of order ideals of a cominuscule poset C where C comes from two of the three infinite families of cominuscule posets or the exceptional cases. We show that the Auslander-Reiten translation τ on the Grothendieck group of the bounded derived category for the incidence algebra of the poset J(C), which is called the Coxeter transf...