Abstract
ABSTRACTThe class of local self-injective algebras of dihedral type generalizes the group algebras of the dihedral 2-groups over fields of characteristic 2. For any such local self-injective dihedral algebra Aq, over any algebraically closed field, we classify the indecomposable string modules that have trivial endomorphism ring in the stable category . As an application we describe the stable Picard group of Aq, which consists of all auto-equivalences of Morita type of . This result can be seen as a generalization of the description of the groups of endo-trivial modules for dihedral 2-groups. Additionally, we show that any algebra stably equivalent of Morita type to a self-injective local dihedral algebra must be Morita equivalent to it.
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