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...
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...
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...
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...
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.
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.
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...
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{...
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...
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...
