Space of second order linear differential operators as a module over the Lie algebra of vector fields

1994/09/12 by C. Duval, Duval, C., V. Ovsienko +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9409065

20 pages, CPT-preprint Marseille

arxiv created 1994/09/12 · arxiv updated 2009/11/30

Abstract

The space of linear differential operators on a smooth manifold M has a natural one-parameter family of Diff(M) (and Vect(M))-module structures, defined by their action on the space of tensor-densities. It is shown that, in the case of second order differential operators, the Vect(M)-module structures are equivalent for any degree of tensor-densities except for three critical values: \0,1\over 2,1\. Second order analogue of the Lie derivative appears as an intertwining operator between the spaces of second order differential operators on tensor-densities.

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