On Derived Equivalence of Algebras of Semidihedral Type with Two Simple Modules

Abstract

The Hochschild cohomology groups of degrees not exceeding 3 are computed for algebras of semidihedral type that form the family SD(2B)₁ (from the famous K. Erdmann’s classification). In the calculation, the beforehand construction of the initial part of the minimal projective bimodule resolution is used for algebras from the family under discussion. The obtained results imply that the algebras from the families SD(2B)₁ and SD(2B)₂ with the same parameters in defining relations are not derived equivalent.