Derived equivalence classification of algebras of dihedral, semidihedral, and quaternion type

Algebras of dihedral, semidihedral, and quaternion type were introduced by K. Erdmann as a generalization of blocks of finite groups of tame representation type. In a series of papers Erdmann gave a description of the Morita equivalence classes of these algebras. The aim of the present article is to present a classification of algebras of dihedral, semidihedral, and quaternion type up to derived equivalence. As an application we can show that all basic algebras in Erdmann's list are actually of tame representation type. (C) 1999 Academic Press.