Applications of Gorenstein projective $\tau$-rigid modules

Hui Liu; Xiaojin Zhang; Yingying Zhang

Applications of Gorenstein projective $\tau$-rigid modules

Representation Theory 2024-01-01 v2 Rings and Algebras

Authors: Hui Liu , Xiaojin Zhang , Yingying Zhang

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.

Keywords

gorenstein projective modules $\tau$-rigid modules $cm$-$\tau$-tilting free algebras tachikawa conjecture homological properties representation theory

Cite

@article{arxiv.2312.15586,
  title  = {Applications of Gorenstein projective $\tau$-rigid modules},
  author = {Hui Liu and Xiaojin Zhang and Yingying Zhang},
  journal= {arXiv preprint arXiv:2312.15586},
  year   = {2024}
}

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Applications of Gorenstein projective $\tau$-rigid modules

Abstract

Keywords

Cite

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