On the classification of symplectic DQ-algebroids

Paul Bressler; Juan Diego Rojas

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arXiv · 2304.03332

On the classification of symplectic DQ-algebroids

Paul Bressler·Juan Diego Rojas

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Abstract

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.

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BibTeX RIS

Paul Bressler, Juan Diego Rojas. 2023-04-06. On the classification of symplectic DQ-algebroids. https://arxiv.org/abs/2304.03332

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