Geodesic
On the classification of symplectic DQ-algebroids
Theory and applications of categories, Tome 38 (2022), pp. 64-100 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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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Classification : 53D55
Keywords: DQ-algebroid, gerbe, deformation quantization 
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     author = {Paul Bressler and Juan Diego Rojas},
     title = {On the classification of symplectic {DQ-algebroids}},
     journal = {Theory and applications of categories},
     pages = {64--100},
     year = {2022},
     volume = {38},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a2/}
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Paul Bressler; Juan Diego Rojas. On the classification of symplectic DQ-algebroids. Theory and applications of categories, Tome 38 (2022), pp. 64-100. http://geodesic.mathdoc.fr/item/TAC_2022_38_a2/