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.

Kvamme, Sondre Marczinzik, René
Published in
Applied Categorical Structures

We review the theory of Co-Gorenstein algebras, which was introduced in Beligiannis (Commun Algebra 28(10):4547–4596, 2000). We show a connection between Co-Gorenstein algebras and the Nakayama and Generalized Nakayama conjecture.

Eisele, Florian Janssens, Geoffrey Raedschelders, Theo
Published in
Mathematische Zeitschrift

We prove a theorem which gives a bijection between the support τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-tilting modules over a given finit...

Chaio, Claudia Meur, Patrick Le Trepode, Sonia

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 in terms of the induced natural transformations between representable functors on this graded cate...

Kalck, Martin Karmazyn, Joseph

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 algebras. As special cases, we obtain a Ringel-duality formula for a family of strongly quasi-hereditary algeb...

Pauksztello, David Saorín, Manuel Zvonareva, Alexandra
Published in
Forum Mathematicum

We show that any bounded t-structure in the bounded derived category of a silting-discrete algebra is algebraic, i.e. has a length heart with finitely many simple objects. As a corollary, we obtain that the space of Bridgeland stability conditions for a silting-discrete algebra is contractible.

Adachi, Takahide Aihara, Takuma Chan, Aaron

Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph algebras which are tilting-discrete.

Giraldo, Hernán
Published in
Algebras and Representation Theory

We describe the irreducible morphisms in the category of modules over a repetitive algebra. We find three special canonical forms: The first canonical form happens when all the component morphisms are split monomorphisms, the second when all the component morphisms are split epimorphisms and the third when there is exactly one irreducible component...

Zhang, Pu
Published in
Science China Mathematics

We clarify the relation between the subcategory Dhfb (A) of homological finite objects in Db(A) and the subcategory Kb(P) of perfect complexes in Db(A), by giving two classes of abelian categories A with enough projective objects such that Dhfb (A) = Kb(P), and finding an example such that Dhfb (A) ≠ Kb(P). We realize the bounded derived category D...