Lie algebroid structures and Lagrangian systems on affine bundles

Journal of Geometry and Physics

Volumn 44, Issue 1, 2002, Pages 70-95

  Martínez, Eduardo ^a   Mestdag, Tom ^b   Sarlet, Willy ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b GHENT UNIVERSITY   (Belgium)

Author keywords

Affine spaces; Lagrangian systems; Lie algebroid; Prolongation

Indexed keywords

EID: 0036837579     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(02)00114-6     Document Type: Article

References (21)

1. A. Cannas da Silva, A. Weinstein, Geometric models for noncommutative algebras, Berkeley Mathematics Lecture Notes 10, American Mathematical Society, Providence, RI, 1999.
2. J.F. Cariñena, L.A. Ibort, G. Marmo, A. Perelomov, On the geometry of Lie algebras and Poisson tensors, J. Phys. A 27 (1994) 7425-7449.
3. T. Courant, Tangent Lie algebroids, J. Phys. A 27 (1994) 4527-4536.
4. M. Crampin, Jet bundle techniques in analytical mechanics, Quaderni del Consiglio Nazionale delle Ricerche 47 (1995).
5. R.L. Fernandes, Lie algebroids, holonomy and characteristic classes, Adv. Math., Preprint, math.DG/0007132, 2000, in press.
6. J. Grabowski, P. Urbanski, Lie algebroids and Poisson-Nijenhuis structures, Rep. Math. Phys. 40 (1997) 195-208.
7. J. Grabowski, K. Grabowska, P. Urbanski, Lie brackets on affine bundles, Preprint, math.DG/0203112, 2002.
8. P.J. Higgins, K. Mackenzie, Algebraic constructions in the category of Lie algebroids, J. Algebra 129 (1990) 194-230.
9. D. Iglesias, J.C. Marrero, Some linear Jacobi structures on vector bundles, C.R. Acad. Sci. Paris Sr. I Math. 331 (2000) 125-130.
10. D. Iglesias, J.C. Marrero, Generalized Lie bi-algebroids and Jacobi structures, J. Geom. Phys. 40 (2001) 176-199.
11. P. Libermann, Lie algebroids and mechanics, Arch. Math. (Brno) 32 (1996) 147-162.
12. K. Mackenzie, Lie groupoids and Lie algebroids in differential geometry, London Math. Soc. Lect. Note Series 124, Cambridge University Press, Cambridge, 1987.
13. K. Mackenzie, Lie algebroids and Lie pseudoalgebras, Bull. London Math. Soc. 27 (1995) 97-147.
14. L. Mangiarotti, G. Sardanashvily, Connections in Classical and Quantum Field Theory, World Scientific Publishing, River Edge, NJ, 2000.
15. E. Martínez, Geometric formulation of mechanics on Lie algebroids, in: Proceedings of the VIII Fall Workshop on Geometry and Physics, Medina del Campo 1999, Publicaciones de las RSME, 2001.
16. E. Martínez, Lagrangian mechanics on Lie algebroids, Acta Appl. Math. 67 (2001) 295-320.
17. E. Martínez, Hamiltonian mechanics on Lie algebroids, Preprint, 2000.
18. M. Popescu, P. Popescu, Geometric Objects Defined by almost Lie Structures, Lie Algebroids, Vol. 54, Banach Center Publications, 2001, pp. 217-233.
19. W. Sarlet, T. Mestdag, E. Martínez, Lagrangian equations on affine Lie algebroids, in: D. Krupka, et al. (Eds.), Differential Geometry and its Applications, Proceedings of the Eighth International Conference, Opava, 2001, in press.
20. W. Sarlet, T. Mestdag, E. Martínez, Lie algebroid structures on a class of affine bundles, Preprint, math. DG/0201264, 2001.
21. A. Weinstein, Lagrangian mechanics and groupoids, in: Mechanics Day (Waterloo, Ont., 1992), Fields Institute Communications, Vol. 7, American Mathematical Society, 1996, pp. 207-231.