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Derived coisotropic structures. II: Stacks and quantization.(English)Zbl 1440.14004

Summary: We extend results about \(n\)-shifted coisotropic structures from Part I [ibid. 24, No. 4, 3061–3118 (2018;Zbl 1461.14006)] of our work to the setting of derived Artin stacks. We show that an intersection of coisotropic morphisms carries a Poisson structure of shift one less. We also compare non-degenerate shifted coisotropic structures and shifted Lagrangian structures and show that there is a natural equivalence between the two spaces in agreement with the classical result. Finally, we define quantizations of \(n\)-shifted coisotropic structures and show that they exist for \(n>1\).

MSC:

14A20 Generalizations (algebraic spaces, stacks)
53D17 Poisson manifolds; Poisson groupoids and algebroids
53D55 Deformation quantization, star products

Citations:

Zbl 1461.14006

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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