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

2008/07/04 by Thorsten Holm, Alexander Zimmermann, Holm, Thorsten +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.0807.0688

arxiv created 2008/07/04 · arxiv updated 2009/12/01

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.

Related

• Generalized Reynolds ideals for non-symmetric algebras
• Derived equivalence classification of symmetric algebras of domestic type
• Invariance of generalised Reynolds ideals under derived equivalences
• Külshammer ideals of algebras of quaternion type
• Ideals in the center of symmetric algebras