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arXiv · 1407.7824

Lie algebras of zero divergence vector fields on complex affine algebraic varieties

Fabrizio Donzelli
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Abstract

For a smooth manifold $X$ equipped with a volume form, let $\dL$ be the Lie algebra of volume preserving smooth vector fields on $X$. A. Lichnerowicz proved that the abelianization of $\dL$ is a finite-dimensional vector space, and that its dimension depends only on the topology of $X$. In this paper we provide analogous results for some classical examples of non-singular complex affine algebraic varieties that admit a nowhere-zero algebraic form of top degree (which plays the role of a volume form).

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Fabrizio Donzelli. 2014-07-29. Lie algebras of zero divergence vector fields on complex affine algebraic varieties. https://arxiv.org/abs/1407.7824

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