Hochschild cohomology of algebras of quaternion type: the family $Q{\left( {2{\mathcal B}} \right)_1}$ in characteristic 3

Abstract

In the present paper, the Hochschild cohomology is investigated for algebras of quaternion type from the family $Q{\left( {2{\mathcal B}} \right)_1}$ over an algebraically closed field of characteristic 3. Using the previously constructed 4-periodic bimodule resolution, we describe the Hochschild cohomology algebra of the above algebras in terms of generators and relations. Bibliography: 11 titles.