2023/12/25 by Liu, Hui, Zhang, Xiaojin, Zhang, Yingying
#16G10 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2312.15586
We first introduce the notion of CM-τ-tilting free algebras as the generalization of CM-free algebras and show the homological properties of CM-τ-tilting free algebras. Then we give a bijection between Gorenstein projective τ-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 τ-rigid modules.