REPETITIVE EQUIVALENCES AND TILTING THEORY

Abstract

Let$R$be a ring and$T$be a good Wakamatsu-tilting module with$S=\text{End}(T_{R})^{op}$. We prove that$T$induces an equivalence between stable repetitive categories of$R$and$S$(i.e., stable module categories of repetitive algebras$\hat{R}$and${\hat{S}}$). This shows that good Wakamatsu-tilting modules seem to behave in Morita theory of stable repetitive categories as that tilting modules of finite projective dimension behave in Morita theory of derived categories.