Quantizations of modules of differential operators

Details Quantizations of modules of differential operators Quantizations of modules of differential operators

2008-10-13

arxiv.org/abs/0810.2156v1

Contemp. Math. 490 (2009), 61-81

Mathematics

Representation Theory

21 pages

Scientific paper

Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal quantization of a V-module of differential operators on M is a decomposition into irreducible A-modules. We survey recent results on projective quantizations and their applications to cohomology, geometric equivalences and symmetries of differential operator modules, and indecomposable modules.

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