Brauer tree algebras and derived equivalence Original Research Article

In this article we introduce the class of the generalised Brauer tree algebras, which is a subclass of the Brauer graph algebras. Our goal is to identify the derived equivalence classes of these algebras. This generalises some previous work by Rickard [9] for blocks with cyclic defect group of a finite modular group algebra. Among the Brauer graph algebras, it is known (see [1] or [2]) that the ones of finite representation type are the Brauer tree algebras. The blocks of cyclic defect of a finite group are Brauer tree algebras.