DQ-algebroids locally defined on a symplectic manifold form a 2-gerbe. By adapting the method of P. Deligne to the setting of DQ-algebroids we show that this 2-gerbe admits a canonical global section, namely that every symplectic manifold admits a canonical DQ-algebroid quantizing the structure sheaf. The construction relies on methods of non-abelian cohomology and local computations in the Weyl algebra. As a corollary we obtain a classification of symplectic DQ-algebroids.
Keywords: DQ-algebroid, gerbe, deformation quantization
2020 MSC: 53D55
Theory and Applications of Categories, Vol. 38, 2022, No. 3, pp 64-100.
Published 2022-01-09.
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