## A construction of Gorenstein projective $\tau $-tilting modules

### Volume 171 / 2023

Colloquium Mathematicum 171 (2023), 103-112
MSC: Primary 16G10; Secondary 18G25.
DOI: 10.4064/cm8682-1-2022
Published online: 21 July 2022

#### 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.