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Higher order jet bundels of lie group-valued functions

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dc.contributor.authorCastrillón López, Marco
dc.contributor.authorRodríguez Abella, Álvaro
dc.date.accessioned2023-06-17T08:28:53Z
dc.date.available2023-06-17T08:28:53Z
dc.date.issued2020
dc.description.abstractFor each positive integer k, the bundle of k-jets of functions from a smooth manifold, X, to a Lie group, G, is denoted by Jk(X,G) and it is canonically endowed with a Lie groupoid structure over X. In this work, we utilize a linear connection to trivialize this bundle, i.e., to build an injective bundle morphism from Jk(X,G) into a vector bundle over G. Afterwards, we give the explicit expression of the groupoid multiplication on the trivialized space, as well as the formula for the inverse element. In the last section, a coordinated chart on X is considered and the local expression of the trivialization is computed.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.statusunpub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/74265
dc.identifier.citation[1] L. Colombo and D. Martín de Diego. Higher-order variational problems on Lie groups and optimal control applications. Journal of Geometric Mechanics, 6(4):451–478, 2014. [2] O. Esen, M. Kudeyt, and S. Sütlü. Second order Lagrangian dynamics on double cross product groups. Journal of Geometry and Physics, 159:103934, 2021. ISSN 0393-0440. doi: https://doi.org/10.1016/j.geomphys.2020.103934. URL https://www.sciencedirect.com/science/article/pii/S0393044020302217. [3] F. Gay-Balmaz, D. Holm, D. Meier, T. Ratiu, and F.-X. Vialard. Invariant higher-order variational problems. Commun. Math. Phys., 309:413–458, 2012. doi: 10.1007/s00220-011-1313-y. [4] B. Hall. Lie Groups, Lie Algebras, and Representations. Graduate Texts in Mathematics. Springer, Cham, second edition, 2015. doi: https://doi.org/10.1007/978-3-319-13467-3. [5] L. Mangiarotti and G. Sardanashvily. Connections in Classical and Quan-tum Field Theory. World Scientific, 2000. doi: 10.1142/2524. URL https://www.worldscientific.com/doi/abs/10.1142/2524. [6] D. J. Saunders. The geometry of jet bundles. Cambridge University Press, 1989. [7] V. S. Varadarajan. Lie Groups, Lie Algebras, and Their Representations. Graduate Texts in Mathematics. Springer, New York, NY, 1 edition, 1984. ISBN 978-1-4612-1126-6. doi: https://doi.org/10.1007/978-1-4612-1126-6. [8] C. Vizman. The group structure for jet bundles over Lie groups. Journal of Lie Theory, 23(3), 2013.
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7247
dc.language.isoeng
dc.relation.projectIDPGC2018-098321-B-I00 and PID2021-126124NB-I00
dc.rights.accessRightsopen access
dc.subject.cdu512.81
dc.subject.keywordFiber bundle
dc.subject.keywordLie groupoid
dc.subject.keywordJet bundle
dc.subject.keywordPartition
dc.subject.keywordTensor product
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmTopología
dc.subject.unesco12 Matemáticas
dc.subject.unesco1210 Topología
dc.titleHigher order jet bundels of lie group-valued functions
dc.typejournal article
dspace.entity.typePublication
relation.isAuthorOfPublication32e59067-ef83-4ca6-8435-cd0721eb706b
relation.isAuthorOfPublication.latestForDiscovery32e59067-ef83-4ca6-8435-cd0721eb706b
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