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Article

Safronov, Pavel
Poisson reduction as a coisotropic intersection. (English). Higher Structures, vol. 1 (2017), issue 1, pp. 87-121
MSC: 17B63, 53D20, 53D55 | MR 3912052 | Zbl 1429.17024 | DOI: 10.21136/HS.2017.04
Keywords:
Poisson reduction; shifted Poisson structure; BRST complex; brace algebra
Summary:
We give a definition of coisotropic morphisms of shifted Poisson (i.e. $\Bbb P_n$) algebras which is a derived version of the classical notion of coisotropic submanifolds. Using this we prove that an intersection of coisotropic morphisms of shifted Poisson algebras carries a Poisson structure of shift one less. Using an interpretation of Hamiltonian spaces as coisotropic morphisms we show that the classical BRST complex computing derived Poisson reduction coincides with the complex computing coisotropic intersection. Moreover, this picture admits a quantum version using brace algebras and their modules: the quantum BRST complex is quasi-isomorphic to the complex computing tensor product of brace modules.
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