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arXiv · 2308.09576

Remarks on $\tau$-tilted versions of the second Brauer-Thrall Conjecture

Calvin Pfeifer
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Abstract

In this short note, we state a stable and a $\tau$-reduced version of the second Brauer-Thrall Conjecture. The former is a slight strengthening of a brick version of the second Brauer-Thrall Conjecture raised by Mousavand and Schroll-Treffinger-Valdivieso. The latter is stated in terms of Geiss-Leclerc-Schr\"oer's generically $\tau$-reduced components and provides a geometric interpretation of a question of Demonet. It follows that the stable second Brauer-Thrall Conjecture implies our $\tau$-reduced second Brauer-Thrall Conjecture. Finally, we prove the reversed implication for the class of E-tame algebras recently introduced by Asai-Iyama.

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Calvin Pfeifer. 2023-08-18. Remarks on $\tau$-tilted versions of the second Brauer-Thrall Conjecture. https://arxiv.org/abs/2308.09576

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