Abstract
The theory of Nambu–Poisson structures on manifolds is extended to the context of Lie algebroids in a natural way based on the derived bracket associated with the Lie algebroid differential. A new way of combining Nambu–Poisson structures and triangular Lie bialgebroids is described in this work. Also, we introduce the concept of a higher order Dirac structure on a Lie algebroid. This allows to describe both Nambu–Poisson structures and Dirac structures on manifolds in the same setting.
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Wade, A. Nambu–Dirac Structures for Lie Algebroids. Letters in Mathematical Physics 61, 85–99 (2002). https://doi.org/10.1023/A:1020735529188
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DOI: https://doi.org/10.1023/A:1020735529188