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Mathematics Subject Classification: 46A13, 46T05, 58A32
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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.24 n.1 San José Jan./Jun. 2017
https://doi.org/10.15517/rmta.v24i1.27747
Artículo
Límites directos de prolongaciones de algebroides de lie
Direct limits of lie algebroids prolongations
1Lycée Pierre de Fermat, Parvis des Jacobins, 31000 Toulouse, France. E-Mail: Patrick.Cabau@ac-toulouse.fr
Probamos que se puede definir estructuras de espacios convenientes sobre límites directos de algebroides de Lie y sus prolongaciones.
Palabras clave: límite directo; algebroide de Lie; prolongación de algebroide de Lie; cálculo diferencial conveniente
We prove that direct limits of Lie algebroids and their prolongations can be endowed with structures of convenient spaces.
Keywords: direct limit; Lie algebroid; prolongation of Lie algebroid; convenient calculus
Referencias
Bourbaki, N. (2006) Eléments de Mathématiques, Algèbre, Chapitres 1 à 3, 2 eme ` édition. Springer, Berlin. [ Links ]
Cabau, P. (2012) “Strong projective limit of Banach Lie algebroids”, Portugal. Math. (N.S.) 69(1): 1-21. [ Links ]
Cabau, P.; Pelletier, F. (2012) “Almost Lie structures on an anchored Banach bundle”, Journal of Geometry and Physics 62(11): 2147-2169. [ Links ]
De las Nieves Sosa Martín, D. (2008) Algebroides de Lie y Mecánica Geométrica. Tesis, Universidad de La Laguna. [ Links ]
De León, M.; Marrero, J.C.; Martínez, E. (2005) “Lagrangian submanifolds and dynamics on Lie algebroids”, J. Phys. A: Math. Gen. 38 (24): R241-R308. [ Links ]
Glöckner, H. (2003) “Direct limit of Lie groups and manifolds”, J. Math. Kyoto Univ. (JMKYAZ) 43(1): 1-26. [ Links ]
Glöckner, H. (2005) “Fundamentals of direct limit Lie theory", Compositio Math. 141(6): 1551-1577 [ Links ]
Glöckner, H. (2007) “Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories”, Journal of Functional Analysis 245(1): 19-61. [ Links ]
Hansen, V.L. (1971) “Some theorems on direct limit of expanding sequences of manifolds”, Math. Scand. 29(1): 5-36. [ Links ]
Higgins, P.J.; Mackenzie, K.C.H. (1990) “Algebraic constructions in the category of Lie algebroids”, J. Algebra 129(1): 194-230. [ Links ]
Iglesias Ponte, D. (2011) “Variedades de Poisson, grupoides y algebroides de Lie”, Actas del XI Congreso Dr. Antonio A.R. Monteiro: 35-59. [ Links ]
Kriegel, A.; Michor, P.W. (1997) The convenient Setting of Global Analysis. AMS Mathematical Surveys and Monographs 53, Providence RI. [ Links ]
Lang, S. (1995) Differential and Riemannian Manifolds, Graduate Texts in Mathematics, 160. Springer, New York. [ Links ]
Magri, F.; Morosi, C. (2008) “A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson-Nijenhuis manifolds”, Quaderno S 19, Università degli Studi di Milano. [ Links ]
Martínez, E. (2005) “Classical field theory on Lie algebroids: multisymplectic formalism”, J. Phys. A: Math. Gen. 38: 7145-7160. [ Links ]
Martínez, E. (2007) “Lie algebroids in classical mechanics and optimal control”, Symmetry, Integrability and Geometry: Methods and Applications SIGMA 3, (5): 1-17. [ Links ]
Pradines, J. (1966) “Théorie de Lie pour les groupoïdes différentiables. Relations entre propriétés locales et globales”, C.R. Acad. Sci. Paris 263(25): 907-910. [ Links ]
Suri, A.; Cabau, P. (2014) “Geometric structure for the tangent bundle of direct limit manifolds”, Differential Geometry - Dynamical Systems 16: 239-247. [ Links ]
Weinstein, A. (1996) “Lagrangian mechanics and groupoids”, Fields Inst. Comm. 7: 207-231. [ Links ]
Recibido: 23 de Junio de 2015; Revisado: 18 de Agosto de 2016; Aprobado: 07 de Octubre de 2016
Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons
