Zhang, Chao
Published in
Science China Mathematics

Bongartz (2013) and Ringel (2011) proved that there is no gaps in the sequence of lengths of indecomposable modules for the finite-dimensional algebras over algebraically closed fields. The present paper mainly studies this "no gaps" theorem as to cohomological length for the bounded derived category Db(A) of a gentle algebra A: if there is an inde...

Ovsienko, Valentin Tabachnikov, Serge
Published in
Algebras and Representation Theory

We investigate a general method that allows one to construct new integer sequences extending existing ones. We apply this method to the classic Somos-4 and Somos-5, and the Gale-Robinson sequences, as well as to more general class of sequences introduced by Fordy and Marsh, and produce a great number of new sequences. The method is based on the not...

Asashiba, Hideto Escolar, Emerson G. Hiraoka, Yasuaki Takeuchi, Hiroshi
Published in
Japan Journal of Industrial and Applied Mathematics

The theory of persistence modules on the commutative ladders CLn(τ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CL_n(\tau )$$\end{document} provides an extension of ...

Chindris, Calin Kinser, Ryan
Published in
Mathematische Annalen

Consider a finite-dimensional algebra A and any of its moduli spaces M(A,d)θss\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {M}}}(A,\mathbf {d})^{ss}_{\the...

Maslovarić, Marcel Seppänen, Henrik
Published in
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

We generalize the notion of multi-Gieseker semistability for coherent sheaves, introduced by Greb, Ross, and Toma, to quiver sheaves for a quiver Q. We construct coarse moduli spaces for semistable quiver sheaves using a functorial method that realizes these as subschemes of moduli spaces of representations of a twisted quiver, depending on Q, with...

Hochenegger, Andreas Kalck, Martin Ploog, David
Published in
Mathematische Zeitschrift

We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe spherical subcategories and their poset structure for derived categories of certain finite-dimensional algebras.

Zito, Stephen
Published in
Archiv der Mathematik

Let C be a finite dimensional algebra with B a split extension by a nilpotent bimodule E. We provide a short proof to a conjecture by Assem and Zacharia concerning properties of modB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage...

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...

Chapoton, Frédéric Rognerud, Baptiste
Published in
Algebras and Representation Theory

In this note, we investigate the representation type of the cambrian lattices and some other related lattices. The result is expressed as a very simple trichotomy. When the rank of the underlined Coxeter group is at most 2, the lattices are of finite representation type. When the Coxeter group is a reducible group of type A13\documentclass[12pt]{mi...

Garver, Alexander McConville, Thomas
Published in
Algebras and Representation Theory

The exchange graph of a 2-acyclic quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. When the quiver admits a nondegenerate Jacobi-finite potential, the exchange graph admits a natural acyclic orientation called the oriented exchange graph, as shown by Brüstle and Yang. The oriented exchange graph is isomorphic ...