Multiplicative structure on the Hochschild cohomology of crossed product algebras

Details Multiplicative structure on the Hochschild cohomology of crossed product algebras Multiplicative structure on the Hochschild cohomology of crossed product algebras

2005-11-15

arxiv.org/abs/math/0511396v2

Mathematics

Quantum Algebra

9 pages; the Gerstenhaber bracket part withdrawn on 12/08/05 due to a gap in one of the proofs. Some references added

Scientific paper

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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