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We prove formulas of different types that allow to calculate the Gerstenhaberbracket on the Hochschild cohomology of an algebra using some arbitraryprojective bimodule resolution for it. Using one of these formulas, we give anew short proof of the derived invariance of the Gerstenhaber algebra structureon Hochschild cohomology. Also we give some new formulas for the Connes'differential on the Hochschild homology that lead to formulas for BVdifferential on the Hochschild cohomology in the case of symmetric algebras.Finally, we use one of the obtained formulas to get a full description of theBV structure and, correspondingly, the Gerstenhaber algebra structure on theHochschild cohomology of a class of symmetric algebras.

Gerstenhaber bracket on the Hochschild cohomology via an arbitrary resolution