There are various proposals for and definitions of higher order generalization of the concept of Poisson brackets.
Dedicated lab entries exist so far for the following cases:
Poisson n-algebra (rationalied En-algebra stucture)
Poisson bracket Lie n-algebra (L-infinity algebra structure)
Definitons analogous to Nambu brackets are discussed in
José de Azcárraga, José M. Izquierdo, J. C. Perez Bueno, On the generalizations of Poisson structures, J. Phys. A 30 (1997) L607-L616 [arXiv:hep-th/9703019, doi:10.1088/0305-4470/30/18/001]
Raúl Ibáñez, Juan C. Marrero, and David Martn de Diego, Dynamics of generalized Poisson and Nambu–Poisson brackets, Journal of Mathematical Physics 38, 2332 (1997); doi: 10.1063/1.531960
Definitions that yield Filippov n-Lie algebras include
Last revised on June 19, 2023 at 14:52:10. See the history of this page for a list of all contributions to it.