THE BV-ALGEBRA STRUCTURE ON THE HOCHSCHILD COHOMOLOGY OF LOCAL ALGEBRAS OF QUATERNION TYPE IN CHARACTERISTIC 2

摘要

This paper is a sequel of the joint paper by the author with S. O. Ivanov, Yu. Volkov, and G. Zhou. In the present paper, the BV-structure, and therefore, the Gerstenhaber algebra structure on the Hochschild cohomology of local algebras of generalized quaternion type is completely described over a field of characteristic 2. The family of algebras under investigation contains group algebras of generalized quaternion groups for which the case of characteristic 2 is the only one where the calculation of Hochschild cohomology and structures on it is a highly nontrivial problem. Also the group algebras of generalized quaternion groups represent classes of Morita-equivalence of tame group blocks from K. Erdmann's classification. In particular, the BV-structure on the Hochschild cohomology of group algebras of some noncommutative groups is described. Bibliography: 22 titles.