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

Thorsten Holm (1) , Alexander Zimmermann (2)

1 Institut fuer Algebra, Zahlentheorie und Diskrete Mathematik
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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.

Domaines: Théorie des représentations [math.RT]

Thorsten Holm, Alexander Zimmermann. Generalized Reynolds ideals and derived equivalences for algebras of dihedral and semidihedral type. Journal of Algebra, 2008, 320 (9), pp.3425-3437. ⟨hal-00293248⟩