Polarized deformation quantization
Abstract
Let $A$ be a star product on a symplectic manifold $(M,\omega_0)$, $\frac{1}{t}[\omega]$ its Fedosov class, where $\omega$ is a deformation of $\omega_0$. We prove that for a complex polarization of $\omega$ 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 $P$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2000
 arXiv:
 arXiv:math/0007186
 Bibcode:
 2000math......7186B
 Keywords:

 Quantum Algebra
 EPrint:
 Latex2e, 23 pp