×

zbMATH — the first resource for mathematics

Some remarks concerning Nambu mechanics. (English) Zbl 0849.70014
Summary: The structure of Nambu-Poisson brackets is studied, and we establish that any Nambu tensor is decomposable. We show that every Nambu-Poisson manifold admits a local foliation by canonical Nambu-Poisson manifolds. Finally, a cohomology for Nambu (Lie) algebras which is adapted to the study of formal deformations of Nambu structures is introduced.

MSC:
70H99 Hamiltonian and Lagrangian mechanics
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Nambu, Y.: Generalized Hamiltonian dynamics, Phys. Rev. D 7 (1973), 2405-2412. · Zbl 1027.70503
[2] Takhtajan, L.: On foundation of the generalized Nambu mechanics, Comm. Math. Phys. 160 (1994), 295-315. · Zbl 0808.70015
[3] Flato, M. and Fronsdal, C.: Unpublished (1992).
[4] Takhtajan, L.: A higher order analog of Chevalley-Eilenberg complex and deformation theory of n-algebras, St. Petersburg Math. J. 6 (1995), 429-438.
[5] Weitzenböck, R.: Invariantentheorie P. Noordhoff, Groningen, 1923.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.