Tilting modules and representation dimensions

In this paper, we compare the representation dimensions of two algebras linked by certain tilting modules. Our main results can be stated as follows: Suppose T is a tilting module over A and B=EndA(T). Then: (1) If T is separating and splitting, then rep.dim(A)=rep.dim(B); (2) If T=P⊕τ−1S is an APR-tilting module and the injective dimension of S is at most 2, then rep.dim(B)⩽rep.dim(A)+1.