On the classification of symplectic DQ-algebroids

Paul Bressler and Juan Diego Rojas

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.


TAC Home