ON THE CLASSIFICATION OF SYMPLECTIC DQ-ALGEBROIDS

ON THE CLASSIFICATION OF SYMPLECTIC DQ-ALGEBROIDS

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 shea...

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Veröffentlicht in:Theory and applications of categories 2022-01, Vol.38 (3), p.64
Hauptverfasser: Bressler, Paul, Rojas, Juan Diego
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Classification
Construction industry
Homology
Manifolds
Topological manifolds
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Rojas, Juan Diego
description 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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subjects Algebra
Classification
Construction industry
Homology
Manifolds
Topological manifolds
title ON THE CLASSIFICATION OF SYMPLECTIC DQ-ALGEBROIDS
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