First Hochschild cohomology group and stable equivalence classification of Morita type of some tame symmetric algebras

We use the dimension and the Lie algebra structure of the first Hochschild cohomology group to distinguish some algebras of dihedral, semi-dihedral and quaternion type up to stable equivalence of Morita type. In particular, we complete the classification of algebras of dihedral type that was mostly determined by Zhou and Zimmermann.

Keywords

stable equivalence of Morita type, algebras of dihedral, semi-dihedral and quaternion type, first Hochschild cohomology group, Lie algebra

2010 Mathematics Subject Classification

16D90, 16E40, 16G99, 17B60

Full Text (PDF format)

Received 29 June 2017

Received revised 26 April 2018

Published 15 August 2018