A construction of Gorenstein projective tau-tilting modules

TL;DR

This paper constructs Gorenstein projective tau-tilting modules using tensor products, identifies classes of non-self-injective algebras with such modules, and explores conditions for CM-tau-tilting finiteness in finite dimensional algebras.

Contribution

It introduces a tensor product construction for Gorenstein projective tau-tilting modules and investigates CM-tau-tilting finiteness related to matrix algebras.

Findings

Constructed Gorenstein projective tau-tilting modules via tensor products.

Identified non-self-injective algebras with non-trivial Gorenstein projective tau-tilting modules.

Established a partial criterion for CM-tau-tilting finiteness involving matrix algebras.

Abstract

We give a construction of Gorenstein projective $\tau$-tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitting non-trivial Gorenstein projective $\tau$-tilting modules. Moreover, we show that a finite dimensional algebra $\Lambda$ over an algebraically closed field is $CM$-$\tau$-tilting finite if $T_n(\Lambda)$ is $CM$-$\tau$-tilting finite which gives a partial answer to a question on $CM$-$\tau$-tilting finite algebras posed by Xie and Zhang.