Poisson reduction as a coisotropic intersection
Poisson reduction as a coisotropic intersection
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作为各向同性交点的泊松约简
DOI：
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发表时间：
2015
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通讯作者：
P. Safronov
中科院分区：
文献类型：
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作者：
P. Safronov
给出了移位泊松代数（即P_n代数）的共同性态射的定义，这是经典的共同性子流形概念的一个派生版本。由此证明了移泊松代数的共同性态射的交集具有少移一次的泊松结构。通过将哈密顿空间解释为共同性态射，我们证明了经典BRST复计算得到的泊松约简与复计算的共同性交集是一致的。此外，该图允许使用双括号代数及其模的量子版本：量子BRST复与双括号模的复计算张量积是拟同构的。
We give a definition of coisotropic morphisms of shifted Poisson (i.e. $P_n$) 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.