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

Cris Negron; Yury Volkov; Sarah Witherspoon

doi:10.4171/jncg/372

JournalsjncgVol. 14, No. 2pp. 531–565

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

Cris Negron
University of North Carolina, Chapel Hill, USA
Yury Volkov
St. Petersburg State University, Russia
Sarah Witherspoon
Texas A&M University, College Station, USA

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

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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.

Cite this article

Cris Negron, Yury Volkov, Sarah Witherspoon, $A_{\infty}$ -coderivations and the Gerstenhaber bracket on Hochschild cohomology. J. Noncommut. Geom. 14 (2020), no. 2, pp. 531–565

DOI 10.4171/JNCG/372