On band modules and $τ$-tilting finiteness

Sibylle Schroll, Hipolito Treffinger, Yadira Valdivieso

Published 2019-11-20Version 1

In this paper 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 $\tau$-tilting finite if and only if no band module is a brick.