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.