Polarized deformation quantization
نویسندگان
چکیده
Let A be a star product on a symplectic manifold (M,ω0), 1 t [ω] its Fedosov class, where ω is a deformation of ω0. We prove that for a complex polarization of ω there exists a commutative subalgebra, O, in A that is isomorphic to the algebra of functions constant along the polarization. Let F (A) consists of elements of A whose commutator with O belongs to O. Then, F (A) is a Lie algebra which is an O-extension of the Lie algebra of derivations of O. We prove a formula which relates the class of this extension, the Fedosov class, and the Chern class of P .
منابع مشابه
Classification of polarized deformation quantizations
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