A (holomorphic) deformation quantization algebroid over a complex symplectic manifold X is a stack locally equivalent to the ring of WKB operators, that is, microdifferential operators with an extra central parameter τ. In this paper, we will show that the (holomorphic) deformation quantization algebroids endowed with an anti-involution are classiﬁed by _H_2(X; k*X), where _k_∗ is a subgroup of the group of invertible series in ℂ[[_τ_−1]]. In the formal case, the analogous classiﬁcation is given by H_2(X; ℂ_X)[[ℏ]]odd , where one sets ℏ = _τ_−1.
Cite this article
Pietro Polesello, Classiﬁcation of Deformation Quantization Algebroids on Complex Symplectic Manifolds. Publ. Res. Inst. Math. Sci. 44 (2008), no. 3, pp. 725–748DOI 10.2977/PRIMS/1216238303