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Derived Equivalence Classification of Algebras of Dihedral, Semidihedral and Quaternion Type

by Holm, Thorsten.

Series: 1997-02, Preprints

18E30 Derived categories, triangulated categories
16G20 Representations of quivers and partially ordered sets
16G60 Representation type (finite, tame, wild, etc.)

Algebras of dihedral, semidihedral and quaternion type were in-
troduced by K. Erdmann as a generalization of blocks of finite groups
of tame representation type. In a series of papers Erdmann gave a
description of the Morita equivalence classes of these algebras. The
aim of the present article is to present a classification of algebras of
dihedral, semidihedral and quaternion type up to derived equivalence.
As an application we can show that all basic algebras in Erdmann's
list are actually of tame representation type.


This paper was published in:
Journal of Algebra 211, 159-205 (1999)