On the classification of symplectic DQ-algebroids
Symplectic Geometry
2023-04-10 v1 Algebraic Topology
Category Theory
Quantum Algebra
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.
Cite
@article{arxiv.2304.03332,
title = {On the classification of symplectic DQ-algebroids},
author = {Paul Bressler and Juan Diego Rojas},
journal= {arXiv preprint arXiv:2304.03332},
year = {2023}
}
Comments
36 pages