Geodesic
$BV$-algebra structure on Hochschild cohomology of local algebras of quaternion type in characteristic 2
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 136-185 
A. A. Ivanov. $BV$-algebra structure on Hochschild cohomology of local algebras of quaternion type in characteristic 2. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 136-185. http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a10/
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     author = {A. A. Ivanov},
     title = {$BV$-algebra structure on {Hochschild} cohomology of local algebras of quaternion type in characteristic~2},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

This paper is a sequel of joint paper by the author with S. O. Ivanov, Yu. Volkov, and G. Zhou. In the present paper $BV$-structure, and therefore, Gerstenhaber algebra structure on 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 case when calculation of Hochschild cohomology and structures on it is a highly non-trivial problem. Also the group algebras of generalized quaternion groups represent classes of Morita-equivalence of tame group blocks from K. Erdmann's classification. So in particular $BV$-structure on Hochschild cohomology of group algebras of some non-commutative groups is described.

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