Displaying similar documents to “On the geometric prequantization of brackets.”

De Rham cohomology and homotopy Frobenius manifolds

Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette (2015)

Journal of the European Mathematical Society

Similarity:

We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.

The BV-algebra of a Jacobi manifold

Izu Vaisman (2000)

Annales Polonici Mathematici

Similarity:

We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give new examples of Lie bialgebroids over Poisson manifolds.

Remarks on the Lichnerowicz-Poisson cohomology

Izu Vaisman (1990)

Annales de l'institut Fourier

Similarity:

The paper begins with some general remarks which include the Mayer-Vietoris exact sequence, a covariant version of the Lichnerowicz-Poisson cohomology, and the definition of an associated Serre-Hochshild spectral sequence. Then we consider the regular case, and we discuss the Poisson cohomology by using a natural bigrading of the Lichnerowicz cochain complex. Furthermore, if the symplectic foliation of the Poisson manifold is either transversally Riemannian or transversally symplectic,...

Isomorphisms of Poisson and Jacobi brackets

Janusz Grabowski (2000)

Banach Center Publications

Similarity:

We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as, for example, those given by Poisson or contact structures. We admit degenerate structures as well, which seems to be new in the literature.