Leibniz algebroid associated with a Nambu - Poisson structure

Journal of Physics A: Mathematical and General

Volumn 32, Issue 46, 1999, Pages 8129-8144

  Ibanez R ^a   De Leon M ^b   Marrero, J C ^c   Padron E ^c  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b INSTITUTO DE MATEMÁTICAS Y FÍSICA FUNDAMENTAL   (Spain)

^c UNIVERSIDAD DE LA LAGUNA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039756622     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/46/310     Document Type: Article

References (32)

1. Alekseevsky D and Guha P 1996 On decomposability of Nambu-Poisson tensor Acta Math. Univ. Commen. 65 1-10
2. Bayen F and Flato M 1975 Remarks concerning Nambu's generalized mechanics Phys. Rev. D 11 3049-53
3. Bhaskara K H and Viswanath K 1988 Calculus on Poisson manifolds Bull. London Math. Soc. 20 68-72
4. Brylinski J L and Zuckerman G 1999 The outer derivation of a complex Poisson manifold J. reine angew. Math. 506 181-9
5. Chatterjee R 1996 Dynamical symmetries and Nambu mechanics Lett. Math. Phys. 36 117-26
6. Chatterjee R and Takhtajan L A 1996 Aspects of classical and quantum Nambu mechanics Lett. Math. Phys. 37 475-82
7. Dalestski Y L and Takhtajan L A 1997 Leibniz and Lie algebra structures for Nambu algebra Lett. Math. Phys. 39 127-41
8. Dufour J-P and Haraki A 1991 Rotationnels et structures de Poisson quadratiques C. R. Acad. Sci. Paris 312 137-40
9. Evens S, Lu J-H and Weinstein A 1999 Transverse measures, the modular class and a cohomology pairing for Lie algebroids Quart. J. Math. to appear
10. Flato M, Dito G and Sternheimer D 1997 Nambu mechanics, n-ary operations and their quantization Deformation Theory and Symplectic Geometry (Mathematical Physics Studies vol 20) (Dordrecht: Kluwer) pp 43-66
11. Gautheron Ph 1996 Some remarks concerning Nambu mechanics Lett. Math. Phys. 37 103-16
12. Grabowski J and Marmo G 1999 Remarks on Nambu-Poisson and Nambu-Jacobi brackets J. Phys. A: Math. Gen. 32 4239-47
13. Grabowski J and Marmo G 1999 On Filippov algebroids and multiplicative Nambu-Poisson structures Preprint math. DG/9902127 (Diff. Geom. Appl. to appear)
14. Ibáñez R, de León M, Marrero J C and Martín de Diego D 1997 Dynamics of generalized Poisson and Nambu-Poisson brackets J. Math. Phys. 38 2332-44
15. Lichnerowicz A 1977 Les variétés de Poisson et leurs algébres de Lie associées J. Differ. Geom. 12 253-300
16. Liu Z J and Xu P 1992 On quadratic Poisson structures Lett. Math. Phys. 26 33-42
17. Loday J L 1992 Cyclic Homology (Grund. Math. Wissen. vol 301) (Berlin: Springer)
18. Loday J L 1993 Une version non commutative des algébres de Lie: les algébres de Leibniz L'Enseignement Math. 39 269-93
19. Loday J L and Pirashvili T 1993 Universal enveloping algebras of Leibniz and (co)-homology Math. Ann. 296 139-58
20. Lodder J M 1998 Leibniz cohomology for differentiable manifolds Ann. Inst. Fourier, Grenoble 48 73-95
21. Mackenzie K 1987 Lie Groupoids and Lie Algebroids in Differential Geometry (London Mathematical Society Lecture Notes Series vol 124) (Cambridge: Cambridge University Press)
22. Marmo G, Vilasi G and Vinogradov A M 1998 The local structure of n-Poisson and n-Jacobi manifolds J. Geom. Phys. 25 141-82
23. Nakanishi N 1998 On Nambu-Poisson manifolds Rev. Math. Phys. 10 499-510
24. Nambu Y 1973 Generalized Hamiltonian dynamics Phys. Rev. D 7 2405-12
25. Takhtajan L 1994 On foundations of the generalized Nambu mechanics Commun. Math. Phys. 160 295-315
26. Vaisman I 1994 Lectures on the Geometry of Poisson Manifolds (Progress in Mathematics vol 118) (Basel: Birkhäuser)
27. Vaisman I 1998 Nambu-Lie groups Preprint math. DG/9812064
28. Weinstein A 1983 The local structure of Poisson manifolds J. Differ. Geom. 18 523-57
29. Weinstein A 1985 J. Differ. Geom. 22 255 (errata and addenda)
30. Weinstein A 1997 The modular automorphism group of a Poisson manifold J. Geom. Phys. 23 379-94
31. Weinstein A 1998 Poisson geometry Differ. Geom. Appl. 9 213-38
32. Xu P 1999 Gerstenhaber algebras and BV-algebras in Poisson geometry Commun. Math. Phys. 200 545-60