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Lie-Rinehart algebras, descent, and quantization

Johannes Huebschmann
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Abstract

A Lie-Rinehart algebra consists of a commutative algebra and a Lie algebra with additional structure which generalizes the mutual structure of interaction between the algebra of functions and the Lie algebra of smooth vector fields on a smooth manifold. Lie-Rinehart algebras provide the correct categorical language to solve the problem whether Kaehler quantization commutes with reduction which, in turn, may be seen as a descent problem.

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Johannes Huebschmann. 2003-03-02. Lie-Rinehart algebras, descent, and quantization. https://arxiv.org/abs/math/0303016

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