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Published online: 2008-09-30
Classiﬁcation of Deformation Quantization Algebroids on Complex Symplectic ManifoldsPietro Polesello (1) Università di Padova, Italy
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 H2(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 H2(X; ℂX)[[ℏ]]odd , where one sets ℏ = τ−1.
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Polesello Pietro: Classiﬁcation of Deformation Quantization Algebroids on Complex Symplectic Manifolds. Publ. Res. Inst. Math. Sci. 44 (2008), 725-748. doi: 10.2977/prims/1216238303