关于第二Brauer-Thrall猜想的τ $\tau$倾斜版本的注释

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-03-17 DOI:10.1112/blms.70048

Calvin Pfeifer

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引用次数: 0

摘要

在这篇简短的笔记中，我们陈述了第二Brauer-Thrall猜想的稳定和τ $\tau$ -简化版本。前者是对Mousavand和schrol - treffinger - valdivieso提出的第二个Brauer-Thrall猜想的轻微强化。后者是根据Geiß-Leclerc-Schröer的一般τ $\tau$ -简化分量来陈述的，并提供了Demonet问题的几何解释。由此可见，稳定的第二Brauer-Thrall猜想隐含了我们的τ $\tau$约简的第二Brauer-Thrall猜想。最后，我们证明了最近由Asai-Iyama引入的E$ E$ -tame代数类的反向含义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Remarks on τ $\tau$ -tilted versions of the second Brauer–Thrall conjecture$

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Remarks on τ $\tau$ -tilted versions of the second Brauer–Thrall conjecture

In this short note, we state a stable and a $τ$ -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–Schröer's generically $τ$ -reduced components and provides a geometric interpretation of a question of Demonet. It follows that the stable second Brauer–Thrall conjecture implies our $τ$ -reduced second Brauer–Thrall conjecture. Finally, we prove the reversed implication for the class of $E$ -tame algebras recently introduced by Asai–Iyama.