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

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

1994-09-12

arxiv.org/abs/hep-th/9409065v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, CPT-preprint Marseille

Scientific paper

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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