$A_{\infty }$-coderivations and the Gerstenhaber bracket on Hochschild cohomology

Abstract

We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber bracket is the graded commutator of infinity coderivations. We thus generalize, to an arbitrary resolution, Stasheff's realization of the Gerstenhaber bracket on Hochschild cohomology as the graded commutator of coderivations on the tensor coalgebra of the algebra.

arXiv comment26 pages; updated references

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Cited by in corpus (2)

• The $B_{\infty }$-structure on the derived endomorphism algebra of the unit in a monoidal category
• Homotopy liftings and Hochschild cohomology of some twisted tensor products