An algebra of deformation quantization for star-exponentials on complex symplectic manifolds

The cotangent bundle T * X to a complex manifold X is classically endowed with the sheaf of k- algebras W-T*X of deformation quantization, where k := W{pt} is a subfield of C[[h,h(-1)]. Here, we construct a new sheaf of k- algebras W-T*X T * X which contains W-T*X as a subalgebra and an extra central parameter t. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If P is any section of order zero of W-T*X, we show that exp(th(-1)P) is well defined in W-T*X(t).