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, J. M. Izquierdo, J. C. Perez Bueno, On the generalizations of Poisson structures, J.Phys. A30 (1997) L607-L616 (arXiv:hep-th/9703019)
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 July 18, 2020 at 14:13:50. See the history of this page for a list of all contributions to it.