Tilting Theory and Selfinjective Algebras

Abstract

Tilting theory is known as a powerful tool for studying representation theory of artin algebras. Though there are no non-trivial tilting modules over selfinjective algebras, we have a way of using tilting theory for trivial extension selfinjective algebras, starting from a tilting module, which is given by constructing equivalent functors between corresponding stable module categories over trivial extension selfinjective algebras of original algebras.