Applications of Gorenstein projective $\tau$-rigid modules

Hui Liu; Xiaojin Zhang; Yingying Zhang

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Applications of Gorenstein projective $\tau$-rigid modules

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arxiv 2312.15586 v2 pith:UZSZUPLR submitted 2023-12-25 math.RT math.RA

Hui Liu , Xiaojin Zhang , Yingying Zhang This is my paper

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abstract

We first introduce the notion of $CM$-$\tau$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$\tau$-tilting free algebras. Then we give a bijection between Gorenstein projective $\tau$-rigid modules and certain modules by using an equivalence established by Kong and Zhang. Finally, we give a partial answer to Tachikawa's first conjecture by using Gorenstein projective $\tau$-rigid modules.

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