BV-differential on Hochschild cohomology of Frobenius algebras
  For a finite-dimensional Frobenius $k$-algebra $R$ with the Nakayama automorphism $\nu$ we define an algebra ${\rm HH}^*(R)^{\nu\uparrow}$. If the order of $\nu$ is not divisible by the characteristic of $k$, this algebra is isomorphic to the Hochschild cohomology algebra of $R$.. We prove that this algebra is a BV-algebra. We use this fact to calculate the Gerstenhaber algebra structure and BV-structure on the Hochschild cohomology algebras of a family of self-injective algebras of tree type $D_n$. 
Yury Volkov
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