Quantizations of modules of differential operators

Abstract

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.

21 pages

References in corpus (2)

• Differential operators on supercircle: conformally equivariant quantization and symbol calculus
• Conformal symbols and the action of contact vector fields over the superline

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