Keywords
Lie algebroid
prolongation of Lie algebroid
convenient calculus
límite directo
algebroide de Lie
prolongación de algebroide de Lie
cálculo diferencial conveniente
How to Cite
Abstract
We prove that direct limits of Lie algebroids and their prolongations can be endowed with structures of convenient spaces.
References
Bourbaki, N. (2006) Eléments de Mathématiques, Algèbre, Chapitres 1 à 3, 2ème édition. Springer, Berlin.
Cabau, P. (2012) “Strong projective limit of Banach Lie algebroids”, Portugal. Math. (N.S.) 69(1): 1–21.
Cabau, P.; Pelletier, F. (2012) “Almost Lie structures on an anchored Banach bundle”, Journal of Geometry and Physics 62(11): 2147–2169.
De las Nieves Sosa Martín, D. (2008) Algebroides de Lie y Mecánica Geométrica. Tesis, Universidad de La Laguna.
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.
Glöckner, H. (2003) “Direct limit of Lie groups and manifolds”, J. Math. Kyoto Univ. (JMKYAZ) 43(1): 1–26.
Glöckner, H. (2005) “Fundamentals of direct limit Lie theory", Compositio Math. 141(6): 1551–1577
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.
Hansen, V.L. (1971) “Some theorems on direct limit of expanding sequences of manifolds”, Math. Scand. 29(1): 5–36.
Higgins, P.J.; Mackenzie, K.C.H. (1990) “Algebraic constructions in the category of Lie algebroids”, J. Algebra 129(1): 194–230.
Iglesias Ponte, D. (2011) “Variedades de Poisson, grupoides y algebroides de Lie”, Actas del XI Congreso Dr. Antonio A.R. Monteiro: 35–59.
Kriegel, A.; Michor, P.W. (1997) The convenient Setting of Global Analysis. AMS Mathematical Surveys and Monographs 53, Providence RI.
Lang, S. (1995) Differential and Riemannian Manifolds, Graduate Texts in Mathematics, 160. Springer, New York. 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.
Martínez, E. (2005) “Classical field theory on Lie algebroids: multisym-plectic formalism”, J. Phys. A: Math. Gen. 38: 7145–7160.
Martínez, E. (2007) “Lie algebroids in classical mechanics and optimal control”, Symmetry, Integrability and Geometry: Methods and Applications SIGMA 3, 050: 1–17.
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.
Suri, A.; Cabau, P. (2014) “Geometric structure for the tangent bundle of direct limit manifolds”, Differential Geometry - Dynamical Systems 16: 239–247.
Weinstein, A. (1996) “Lagrangian mechanics and groupoids”, Fields Inst. Comm. 7: 207–231.