Natural differential operations on manifolds: an algebraic approach

Pavel I. Katsylo; Dmitri A. Timashev

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Natural differential operations on manifolds: an algebraic approach

Pavel I. Katsylo·Dmitri A. Timashev

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Abstract

We consider natural algebraic differential operations acting on geometric quantities over smooth manifolds. We introduce a method of study and classification of such operations, called IT-reduction. It reduces the study of natural operations to the study of polynomial maps between (vector) spaces of jets which are equivariant with respect to certain algebraic groups. Using the IT-reduction, we obtain short and conceptual proofs of some known results on the classification of certain natural operations (the Schouten theorem, etc) together with new results including the non-existence of a universal deformation quantization on Poisson manifolds.

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BibTeX RIS

Pavel I. Katsylo, Dmitri A. Timashev. 2006-07-04. Natural differential operations on manifolds: an algebraic approach. https://arxiv.org/abs/math/0607074

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