Derived equivalence classification of symmetric algebras of domestic type

2005/11/09 by Thorsten Holm, Holm, Thorsten, Andrzej Skowronski +1
Mathematics · #16D50 #16G60 #18E30 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16D50 #msc:16G60 #msc:18E30

paper · pdf · doi:10.48550/arxiv.math/0511227

19 pages

arxiv created 2005/11/09 · arxiv updated 2009/12/01

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. K"ulshammer for symmetric algebras in positive characteristic, and recently shown by A. Zimmermann (math.RA/0509580) to be invariants under derived equivalences.

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