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- W2951878502 abstract "An anologue of the Calabi invariant for Poisson manifolds is considered. For any Poisson manifold $P$, the Poisson bracket on $C^{infty}(P)$ extends to a Lie bracket on the space $Omega^{1}(P)$ of all differential one-forms, under which the space $Z^{1}(P)$ of closed one-forms and the space $B^{1}(P)$ of exact one-forms are Lie subalgebras. These Lie algebras are related by the exact sequence: $$0lon reals lon C^{infty}(P)stackrel{d}{lon} Z^{1}(P)stackrel{f}{lon} H^{1}(P, reals)lon 0, $$ where $H^{1}(P,reals)$ is considered as a trivial Lie algebra, and $f$ is the map sending each closed one-form to its cohomology class. The goal of the present paper is to lift this exact sequence to the group level for compact Poisson manifolds under certain integrability condition. In particular, we will give a geometric description of a Lie group integrating the underlying Poisson algebra $C^{infty}(P) $." @default.
- W2951878502 created "2019-06-27" @default.
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- W2951878502 date "1996-05-05" @default.
- W2951878502 modified "2023-09-27" @default.
- W2951878502 title "Flux homomorphism on symplectic groupoids" @default.
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