Nambu-Dirac structures for Lie algebroids

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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.

Original languageEnglish (US)
Pages (from-to)85-99
Number of pages15
JournalLetters in Mathematical Physics
Issue number2
StatePublished - Aug 1 2002

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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