# New generalized Poisson structures

@article{Azcrraga1996NewGP, title={New generalized Poisson structures}, author={Jos{\'e} Adolfo de Azc{\'a}rraga and A. M. Perelomov and J. C. P{\'e}rez Bueno}, journal={Journal of Physics A}, year={1996}, volume={29} }

New generalized Poisson structures are introduced by using suitable skew-symmetric contravariant tensors of even order. The corresponding `Jacobi identities' are provided by conditions on these tensors, which may be understood as cocycle conditions. As an example, we provide the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras.

## 63 Citations

THE SCHOUTEN-NIJENHUIS BRACKET, COHOMOLOGY AND GENERALIZED POISSON STRUCTURES

- Mathematics, Physics
- 1996

Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten - Nijenhuis bracket. The associated `Jacobi…

Generalized Jacobi structures

- Mathematics, Physics
- 1997

Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions.…

Dynamics of generalized Poisson and Nambu–Poisson brackets

- Mathematics
- 1997

A unified setting for generalized Poisson and Nambu–Poisson brackets is discussed. It is proved that a Nambu–Poisson bracket of even order is a generalized Poisson bracket. Characterizations of…

Homology and cohomology on generalized Poisson manifolds

- Mathematics
- 1998

The canonical homology of a generalized Poisson manifold is introduced, and the two spectral sequences associated with the periodic double complex are studied. The generalized Poisson cohomology is…

Homology and cohomology on generalized Poisson manifolds

- Mathematics
- 1998

The canonical homology of a generalized Poisson manifold is introduced, and the two spectral sequences associated with the periodic double complex are studied. The generalized Poisson cohomology is…

GENERALIZED n-POISSON BRACKETS ON A SYMPLECTIC MANIFOLD

- Physics, Mathematics
- 1998

On a symplectic manifold (M,ω) we study a family of generalized Poisson brackets associated with 2k-forms ωk. The extreme cases are related to the Hamiltonian and Liouville dynamics. We show that the…

Simple Facts Concerning Nambu Algebras

- Mathematics
- 1998

Abstract:A class of substitution equations arising in the extension of Jacobi identity for $n$-gebras is studied and solved. Graded bracket and cohomology adapted to the study of formal deformations…

Higher order simple Lie algebras

- Mathematics, Physics
- 1997

It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their…

Nambu-Jacobi and generalized Jacobi manifolds

- Mathematics
- 1998

The geometry of Nambu-Jacobi and generalized Jacobi manifolds is studied. A large collection of examples is given. The characteristic distribution generated by the Hamiltonian vector fields on a…

On higher Poisson and Koszul--Schouten brackets

- Mathematics, Physics
- 2009

In this note we show how to construct a homotopy BV-algebra on the algebra of differential forms over a higher Poisson manifold. The Lie derivative along the higher Poisson structure provides the…

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