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

by Holm, Thorsten, Zimmermann, Alexander.

Series: 2007-10, Preprints

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

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.

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