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Multiplicative structure on the Hochschild cohomology of crossed product algebras

Rina Anno
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Abstract

Consider a smooth affine algebraic variety $X$ over an algebraically closed field, and let a finite group $G$ act on it. We assume that the characteristic of the field is greater than the dimension of $X$ and the order of $G$. An explicit formula for multiplication on the Hochschild cohomology of a crossed product of $k[G]$ and $k[X]$ is given in terms of multivector fields on $X$ and $g$-invariant subvarieties of $X$ for $g\in G$.

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Rina Anno. 2005-12-08. Multiplicative structure on the Hochschild cohomology of crossed product algebras. https://arxiv.org/abs/math/0511396

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