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

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arxiv 1805.03167 v3 pith:VYNBRFPY submitted 2018-05-08 math.RT math.RA

C. Negron , Y. Volkov , S. Witherspoon This is my paper · ORCID
classification math.RTmath.RA
keywords coderivationsalgebrabracketcohomologygerstenhaberhochschildarbitrarycommutator
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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.

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  1. The Gerstenhaber bracket and cycles in the module category of a monomial quadratic algebra

    math.RT 2019-08 conditional novelty 7.0 of 10

    For monomial quadratic algebras, the circle product underlying the Gerstenhaber bracket of two basic cochains matches a composition operation on the associated cycles in the module category.

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