2006/07/04 by Pavel I. Katsylo, Katsylo, Pavel I., Dmitri A. Timashev +1
Mathematics · #53A55 (Primary) #53D55 (Secondary) #58A20 #58A32 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG #msc:53A55 #msc:53D55 #msc:58A20 #msc:58A32
paper · pdf · doi:10.48550/arxiv.math/0607074
AmSLaTeX, 22 pages, 23 bibliography items
arxiv created 2006/07/04 · arxiv updated 2009/12/01
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.