07-10

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

by Holm, Thorsten; Zimmermann, Alexander

 

Preprint series: 07-10, Preprints

MSC:
16G10 Representations of Artinian rings
20C05 Group rings of finite groups and their modules, See Also { 16S34}
18E30 Derived categories, triangulated categories
16G60 Representation type (finite, tame, wild, etc.)

 

Abstract: 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.

Keywords: Algebras of dihedral and semidihedral type; Blocks of finite groups; Tame representation type; Derived equivalences; Generalized Reynolds ideals


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