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arXiv · 1911.09021

On band modules and $τ$-tilting finiteness

Sibylle Schroll·Hipolito Treffinger·Yadira Valdivieso
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Abstract

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.

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BibTeXRIS

Sibylle Schroll, Hipolito Treffinger, Yadira Valdivieso. 2020-12-19. On band modules and $τ$-tilting finiteness. https://arxiv.org/abs/1911.09021

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