TY - JOUR

T1 - Generalized Reynolds ideals and derived equivalences for algebras of dihedral and semidihedral type

AU - Holm, Thorsten

AU - Zimmermann, Alexander

N1 - Funding Information: The authors are supported by a German–French grant DAAD-PROCOPE, DAAD grant number D/0628179, and “partenariat Hubert Curien PROCOPE dossier 14765WB” respectively. We gratefully acknowledge the financial support which made the present work possible.

PY - 2008/11/1

Y1 - 2008/11/1

N2 - Generalized Reynolds ideals are ideals of the center of a symmetric algebra over a field of positive characteristic. They have been shown by the second author to be invariant under derived equivalences. In this paper we determine the generalized Reynolds ideals of algebras of dihedral and semidihedral type (as defined by Erdmann), in characteristic 2. In this way we solve some open problems about scalars occurring in the derived equivalence classification of these algebras.

AB - Generalized Reynolds ideals are ideals of the center of a symmetric algebra over a field of positive characteristic. They have been shown by the second author to be invariant under derived equivalences. In this paper we determine the generalized Reynolds ideals of algebras of dihedral and semidihedral type (as defined by Erdmann), in characteristic 2. In this way we solve some open problems about scalars occurring in the derived equivalence classification of these algebras.

KW - Algebras of dihedral and semidihedral type

KW - Blocks of finite groups

KW - Derived equivalences

KW - Generalized Reynolds ideals

KW - Tame representation type

UR - http://www.scopus.com/inward/record.url?scp=52749084464&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2008.07.026

DO - 10.1016/j.jalgebra.2008.07.026

M3 - Article

AN - SCOPUS:52749084464

VL - 320

SP - 3425

EP - 3437

JO - Journal of algebra

JF - Journal of algebra

SN - 0021-8693

IS - 9

ER -