2019/11/20 by Sibylle Schroll, Hipolito Treffinger, Schroll, Sibylle +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1911.09021
openalex publication_date 2019/11/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper, motivated by a τ-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 τ-tilting finite if and only if no band module is a brick. We also recover a criterion for the τ-tilting finiteness of Brauer graph algebras in terms of the Brauer graph.