Nambu-Dirac Structures on Lie Algebroids

Details Nambu-Dirac Structures on Lie Algebroids Nambu-Dirac Structures on Lie Algebroids

2002-04-25

arxiv.org/abs/math/0204310v2

Mathematics

Symplectic Geometry

minor corrections

Scientific paper

The theory of Nambu-Poisson structures on manifolds is extended to the context of Lie algebroids, in a natural way based on the Vinogradov bracket associated with Lie algebroid cohomology. We show that, under certain assumptions, any Nambu-Poisson structure on a Lie algebroid is decomposable.Also, we introduce the concept of a higher order Dirac structure on a Lie algebroid. This allows to describe both Nambu-Poisson structures on Lie algebroids and Dirac structures on manifolds in the same setting.

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