Natural differential operations on manifolds: an algebraic approach

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dc.creatorKatsylo, Pavel I.
dc.creatorTimashev, Dmitri A.
dc.date2006-07-04
dc.date.accessioned2026-07-07T07:17:58Z
dc.date.available2026-07-07T07:17:58Z
dc.descriptionWe 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.
dc.descriptionAmSLaTeX, 22 pages, 23 bibliography items
dc.identifierhttps://arxiv.org/abs/math/0607074
dc.identifierhttp://arxiv.org/abs/math/0607074
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114138
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.subject53A55 (Primary); 58A20, 58A32, 53D55 (Secondary)
dc.titleNatural differential operations on manifolds: an algebraic approach
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