On band modules and $\tau$-tilting finiteness
Abstract
In this paper, motivated by a -tilting version of the Brauer-Thrall Conjectures, we study general properties of band modules and their endomorphisms in the module category of a finite dimensional algebra. As an application we describe properties of torsion classes containing band modules. Furthermore, we show that a special biserial algebra is -tilting finite if and only if no band module is a brick. We also recover a criterion for the -tilting finiteness of Brauer graph algebras in terms of the Brauer graph.
Keywords
Cite
@article{arxiv.1911.09021,
title = {On band modules and $\tau$-tilting finiteness},
author = {Sibylle Schroll and Hipolito Treffinger and Yadira Valdivieso},
journal= {arXiv preprint arXiv:1911.09021},
year = {2020}
}
Comments
To appear in Mathematische Zeitschrift. Substantial re-write: introduced tau-tilting version of the Brauer-Thrall conjectures for finite dimensional algebras and proof of the conjectures for special biserial algebras; removed Proposition 3.1 which contained a mistake; new proof of the criterion of tau-tilting finiteness for special biserial algebras