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

Abstract

We give a construction of Gorenstein projective τ -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 τ -tilting modules. Moreover, we show that a finite dimensional algebra Λ over an algebraically closed field is CM -τ -tilting finite if Tn(Λ) is CM -τ -tilting finite which gives a partial answer to a question on CM -τ -tilting finite algebras posed by Xie and Zhang.