A 𝜏-tilting approach to the first Brauer-Thrall conjecture

Schroll, Sibylle; Treffinger, Hipolito

doi:10.1090/proc/16055

A $\tau$-tilting approach to the first Brauer-Thrall conjecture
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by Sibylle Schroll and Hipolito Treffinger PDF

Proc. Amer. Math. Soc. 150 (2022), 4567-4574 Request permission

Abstract:

In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length of all such modules is bounded.

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