A_∞-coderivations and the Gerstenhaber bracket on Hochschild cohomology

2018/05/08 by Cris Negron, Negron, C., Yury Volkov +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1805.03167

openalex publication_date 2018/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Hochschild cohomology of group extensions of quantum complete intersections

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