Displaying similar documents to “The BV-algebra of a Jacobi manifold”

On characterization of Poisson and Jacobi structures

Janusz Grabowski, Paweŀ Urbański (2003)

Open Mathematics

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We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.

Isomorphisms of Poisson and Jacobi brackets

Janusz Grabowski (2000)

Banach Center Publications

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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.

Some Remarks on Dirac Structures and Poisson Reductions

Zhang-Ju Liu (2000)

Banach Center Publications

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Dirac structures are characterized in terms of their characteristic pairs defined in this note and then Poisson reductions are discussed from the point of view of Dirac structures.

Modular vector fields and Batalin-Vilkovisky algebras

Yvette Kosmann-Schwarzbach (2000)

Banach Center Publications

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We show that a modular class arises from the existence of two generating operators for a Batalin-Vilkovisky algebra. In particular, for every triangular Lie bialgebroid (A,P) such that its top exterior power is a trivial line bundle, there is a section of the vector bundle A whose d P -cohomology class is well-defined. We give simple proofs of its properties. The modular class of an orientable Poisson manifold is an example. We analyse the relationships between generating operators of the...

Poisson Lie groups and their relations to quantum groups

Janusz Grabowski (1995)

Banach Center Publications

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The notion of Poisson Lie group (sometimes called Poisson Drinfel'd group) was first introduced by Drinfel'd [1] and studied by Semenov-Tian-Shansky [7] to understand the Hamiltonian structure of the group of dressing transformations of a completely integrable system. The Poisson Lie groups play an important role in the mathematical theories of quantization and in nonlinear integrable equations. The aim of our lecture is to point out the naturality of this notion and to present basic...