First Hochschild cohomology group and stable equivalence classification of Morita type of some tame symmetric algebras. (English) Zbl 1433.16006
Summary: 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 G. Zhou and A. Zimmermann [J. Pure Appl. Algebra 215, No. 12, 2969–2986 (2011; Zbl 1257.16014)].
MSC:
| 16D90 | Module categories in associative algebras |
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
| 16G99 | Representation theory of associative rings and algebras |
| 17B60 | Lie (super)algebras associated with other structures (associative, Jordan, etc.) |
