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On characterization of Poisson and Jacobi structures. (English) Zbl 1028.17015

The authors give a characterization of Poisson and Jacobi structures by means of complete (tangent) lifts of the corresponding tensors. In [J. Phys. A., Math. Gen. 28, 6743–6777 (1995; Zbl 0872.58028)], the authors obtained a characterization of Poisson tensors on \(T*M\), for a smooth manifold \(M\), by means of the tangent lift of contravariant tensors. The aim of this paper is to generalize this characterization in order to include Jacobi structures.
In the first section, the authors recall some general facts about Lie and Jacobi algebroids. Then they obtain a characterization of Poisson and Jacobi structures in terms of tangent lifts, related to canonical structures by morphisms of vector bundles. It is then shown that a similar characterization holds for canonical structures associated with Lie algebroids and Jacobi algebroids.

MSC:

17B62 Lie bialgebras; Lie coalgebras
53D17 Poisson manifolds; Poisson groupoids and algebroids
58H05 Pseudogroups and differentiable groupoids

Citations:

Zbl 0872.58028
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References:

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