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Gerstenhaber bracket on double Hochschild complex and deformation theory

Boris Shoikhet
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Abstract

We construct a differential and a Lie bracket on the space\linebreak $\{\Hom (A^{\otimes k}, A^{\otimes l})\},_{k,l\ge 0}$ for any associative algebra $A$. The restriction of this bracket to the space $\{\Hom (A^{\otimes k}, A)\},_{k\ge 0}$ is exactly the Gerstenhaber bracket. We discuss some formality conjecture related with this construction. We also discuss some applications to deformation theory.

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Boris Shoikhet. 1999-10-07. Gerstenhaber bracket on double Hochschild complex and deformation theory. https://arxiv.org/abs/math/9910043

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