nLab higher Poisson structure

There are various proposals for and definitions of higher order generalization of the concept of Poisson brackets.

Dedicated $n$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

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Definitions that yield Filippov n-Lie algebras include

• Janusz Grabowski, Giuseppe Marmo, On Filippov algebroids and multiplicative Nambu-Poisson structures, Differ. Geom. Appl. 12:35-50,2000 (arXiv:math/9902127)