Details
| Original language | English |
|---|---|
| Pages (from-to) | 3425-3437 |
| Number of pages | 13 |
| Journal | Journal of algebra |
| Volume | 320 |
| Issue number | 9 |
| Publication status | Published - 1 Nov 2008 |
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, Derived equivalences, Generalized Reynolds ideals, Tame representation type
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of algebra, Vol. 320, No. 9, 01.11.2008, p. 3425-3437.
Research output: Contribution to journal › Article › Research › peer review
}
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 -