On Filippov algebroids and multiplicative Nambu-Poisson structures

Differential Geometry and its Application

Volumn 12, Issue 1, 2000, Pages 35-50

  Grabowski, J ^a   Marmo, G ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Lie algebroid; Multiplicative tensor; n ary operation; Nambu Poisson bracket

Indexed keywords

EID: 0033632733     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0926-2245(99)00042-X     Document Type: Article

References (27)

1. D. Alexeevsky and P. Guha, On decomposability of Nambu-Poisson tensor, Acta Math. Univ. Comenian. 65 (1996) 1-9.
2. J.A. Azcárraga, J.M. Izquierdo and J.C. Pérez Bueno, On the higher-order generalizations of Poisson structures, J. Phys. A 30 (1997) L607-L616.
3. J.A. Azcárraga, A.M. Perelomov and J.C. Pérez Bueno, New generalized Poisson structures, J. Phys. A 29 (1996) 627-649.
4. F. Bayen and M. Flato, Remarks concerning Nambu's generalized mechanics, Phys. Rev. D 11 (1975) 3049-3053.
5. R. Chatterjee, Dynamical symmetries and Nambu mechanics, Lett. Math. Phys. 36 (1996) 117-126.
6. Y.L. Daletskii and L. Takhtajan, Leibniz and Lie algebra structures for Nambu algebra, Lett. Math. Phys. 39 (1997) 127-141.
7. J.-P. Dufour and N.T. Zung, Linearization of Nambu Structures, Preprint, Univ. Montpellier, 1997.
8. V.T. Filippov, n-Lie algebras, Sibirsk. Math. Zh. 26 (6) (1985) 126-140.
9. M. Flato, G. Dito and D. Sternheimer, Nambu Mechanics, n-ary Operations and their Quantization, Preprint q-alg/9703019.
10. P. Gautheron, Some remarks concerning Nambu mechanics, Lett. Math. Phys. 37 (1996) 103-116.
11. J. Grabowski, Abstract Jacobi and Poisson structures, J. Geom. Phys. 9 (1992) 45-73.
12. J. Grabowski and G. Marmo, Remarks on Nambu-Poisson and Nambu-Jacobi brackets, J. Phys. A 32 (1999) 4239-4247.
13. J. Grabowski and P. Urbański, Tangent lifts of Poisson and related structures, J. Phys. A 28 (1995) 6743-6777.
14. J. Grabowski and P. Urbański, Tangent and cotangent lifts and graded Lie algebras associated with Lie algebroids, Ann. Global Anal. Geom. 15 (1997) 447-486.
15. P. Hanlon and M.L. Wachs, On Lie k-algebras, Adv. in Math. 113 (1995) 206-236.
16. R. Ibánez, M. de León, J.C. Marrero and D. Martín de Diego, Dynamics of generalized Poisson and Nambu-Poisson brackets, J. Math. Phys. 38 (1997) 2332-2344.
17. G. Marmo, G. Vilasi and A.M. Vinogradov, The local structure of n-Poisson and n-Jacobi manifolds, J. Geom. Phys. 25 (1998) 141-182.
18. P.W. Michor and A.M. Vinogradov, n-ary Lie and associative algebras, Rend. Sem. Mat. Univ. Politec Torino 53 (1996) 373-392.
19. N. Nakanishi, On Nambu-Poisson manifolds, Rev. Math. Phys. 10 (1998) 499-510.
20. N. Nakanishi, Nambu-Poisson Tensor on Lie Groups, Preprint, Dept. Math. Gifu-Keizai Univ., 1998.
21. N. Nambu, Generalized Hamiltonian mechanics, Phys. Rev. D 7 (1973) 2405-2412.
22. A. Panov, Multiple Poisson brackets, Vestnik Samarskogo Gosudarstvennogo Universiteta 2 (1996) 33-42 (in Russian).
23. D. Sahoo and M.C. Valsakumar, Nambu mechanics and its quantization, Phys. Rev. A 46 (1992) 4410-4412.
24. M. Schlesinger and J.D. Stasheff, The Lie algebra structure of tangent cohomology and deformation theory, J. Pure Appl. Algebra 38 (1985) 313-322.
25. L. Takhtajan, On foundation of the generalized Nambu mechanics, Commun. Math. Phys. 160 (1994) 295-315.
26. I. Vaisman, Nambu-Lie groups, Preprint, Univ. of Haifa, 1998.
27. A. Vinogradov and M. Vinogradov, On multiple generalizations of Lie algebras and Poisson manifolds, in: M. Henneaux, J. Krasil'shchik and A. Vinogradov, eds., Secondary Calculus and Cohomological Physics, Proc. Conf. Moscow, 1997, Contemporary Mathematics 219 (Amer. Math. Soc., Providence, 1998) 273-287.