Lie-Rinehart and Hochschild cohomology for algebras of differential operators

Francisco Kordon; Thierry Lambre

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arXiv · 2006.01218

Lie-Rinehart and Hochschild cohomology for algebras of differential operators

Francisco Kordon·Thierry Lambre

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Abstract

Let $(S,L)$ be a Lie-Rinehart algebra such that $L$ is $S$-projective and let $U$ be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of $U$ with values on a $U$-bimodule $M$ and whose second page involves the Lie-Rinehart cohomology of the algebra and the Hochschild cohomology of $S$ with values on $M$. After giving a convenient description of the involved algebraic structures we use the spectral sequence to compute explicitly the Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of three lines.

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BibTeX RIS

Francisco Kordon, Thierry Lambre. 2020-06-01. Lie-Rinehart and Hochschild cohomology for algebras of differential operators. https://arxiv.org/abs/2006.01218

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