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BV-differential on Hochschild cohomology of Frobenius algebras (1405.5155v1)
Published 20 May 2014 in math.KT and math.RA
Abstract: 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 $D_n$.