A cohomological construction of modules over Fedosov deformation quantization algebra

Abstract

In certain neighborhood $U$ of an arbitrary point of a symplectic manifold $M$ we construct a Fedosov-type star-product ${\ast }_L$ such that for an arbitrary leaf $\wp$ of a given polarization $\mathcal{D}\subset TM$ the algebra $C^{\infty }(\wp \cap U)[[h]]$ has a natural structure of left module over the deformed algebra $(C^{\infty }(U)[[h]],{\ast }_L)$. With certain additional assumptions on $M$, ${\ast }_L$ becomes a so-called star-product with separation of variables.

8 pages, latex. Final version to appear in IJGMMP

References in corpus (2)

• Wick type deformation quantization of Fedosov manifolds
• Fedosov Quantization on Symplectic Ringed Spaces