Derived equivalence classification of symmetric algebras of domestic type

Abstract

We give a complete derived equivalence classification of all symmetric algebras of domestic representation type over an algebraically closed field. This completes previous work by R. Bocian and the authors, where in this paper we solve the crucial problem of distinguishing standard and nonstandard algebras up to derived equivalence. Our main tool are generalized Reynolds ideals, introduced by B. Külshammer for symmetric algebras in positive characteristic, and recently shown by A. Zimmermann to be invariants under derived equivalences.