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arXiv · 1905.01871

Three results for tau-rigid modules

Zongzhen Xie·Libo Zan·Xiaojin Zhang
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Abstract

$τ$-rigid modules are essential in the $τ$-tilting theory introduced by Adachi, Iyama and Reiten. In this paper, we give equivalent conditions for Iwanaga-Gorenstein algebras with self-injective dimension at most one in terms of $τ$-rigid modules. We show that every indecomposable module over iterated tilted algebras of Dynkin type is $τ$-rigid. Finally, we give a $τ$-tilting theorem on homological dimension which is an analog to that of classical tilting modules.

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Zongzhen Xie, Libo Zan, Xiaojin Zhang. 2019-05-06. Three results for tau-rigid modules. https://arxiv.org/abs/1905.01871

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