Symmetries and reductions of Dirac-Jacobi structures

In this manuscript we study reductions of Dirac-Jacobi structures on a smooth manifold under the presence of symmetries given by the action of a connected Lie group. The main tools we used are the called "homogenization trick" and the well known reduction of Dirac structures. We show two p...

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Autores:: Yela Rosero, Darlyn Yamid

Tipo de recurso:

Fecha de publicación:: 2021

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: eng

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dc.title.eng.fl_str_mv	Symmetries and reductions of Dirac-Jacobi structures
dc.title.translated.spa.fl_str_mv	Simetrías y reducciones de estructuras Dirac-Jacobi
title	Symmetries and reductions of Dirac-Jacobi structures
spellingShingle	Symmetries and reductions of Dirac-Jacobi structures 510 - Matemáticas::516 - Geometría Physics Quantum theory Física Teoría cuántica Dirac-Jacobi structures Dirac structures Dirac-ization trick Homogenization trick Reduction Estructuras Dirac-Jacobi Estructuras Dirac Truco de homogenización Truco de Dirac-ización Reducción Geometría Geometry
title_short	Symmetries and reductions of Dirac-Jacobi structures
title_full	Symmetries and reductions of Dirac-Jacobi structures
title_fullStr	Symmetries and reductions of Dirac-Jacobi structures
title_full_unstemmed	Symmetries and reductions of Dirac-Jacobi structures
title_sort	Symmetries and reductions of Dirac-Jacobi structures
dc.creator.fl_str_mv	Yela Rosero, Darlyn Yamid
dc.contributor.advisor.none.fl_str_mv	Martínez Alba, Nicolás
dc.contributor.author.none.fl_str_mv	Yela Rosero, Darlyn Yamid
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas::516 - Geometría
topic	510 - Matemáticas::516 - Geometría Physics Quantum theory Física Teoría cuántica Dirac-Jacobi structures Dirac structures Dirac-ization trick Homogenization trick Reduction Estructuras Dirac-Jacobi Estructuras Dirac Truco de homogenización Truco de Dirac-ización Reducción Geometría Geometry
dc.subject.lemb.eng.fl_str_mv	Physics Quantum theory
dc.subject.lemb.spa.fl_str_mv	Física Teoría cuántica
dc.subject.proposal.eng.fl_str_mv	Dirac-Jacobi structures Dirac structures Dirac-ization trick Homogenization trick Reduction
dc.subject.proposal.spa.fl_str_mv	Estructuras Dirac-Jacobi Estructuras Dirac Truco de homogenización Truco de Dirac-ización Reducción
dc.subject.unesco.spa.fl_str_mv	Geometría
dc.subject.unesco.eng.fl_str_mv	Geometry
description	In this manuscript we study reductions of Dirac-Jacobi structures on a smooth manifold under the presence of symmetries given by the action of a connected Lie group. The main tools we used are the called "homogenization trick" and the well known reduction of Dirac structures. We show two particular cases, namely, reduction by moment map and the case when the base manifold is endowed with a contact 1-form.
publishDate	2021
dc.date.accessioned.none.fl_str_mv	2021-10-06T19:34:26Z
dc.date.available.none.fl_str_mv	2021-10-06T19:34:26Z
dc.date.issued.none.fl_str_mv	2021-10-04
dc.type.spa.fl_str_mv	Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv	Text
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dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/80403
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/80403 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	eng
language	eng
dc.relation.references.spa.fl_str_mv	A. A. Belavin and V. G. Drinfeld, Solutions of the classical Yang–Baxter equa- tion for simple Lie algebras, Funktsional’nyi Analiz i ego Prilozheniya, 16 (1982), pp. 1–29. H. Bursztyn, A brief introduction to Dirac manifolds, Geometric and topological methods for quantum field theory, (2013), pp. 4–38. H. Bursztyn, G. R. Cavalcanti, and M. Gualtieri, Reduction of Courant algebroids and generalized complex structures, Advances in Mathematics, 211 (2007), pp. 726–765. J. Costa and F. Petalidou, Twisted Jacobi manifolds, twisted Dirac-Jacobi structures and quasi-Jacobi bialgebroids, Journal of Physics. A, Mathematical and General, 39 (2006). T. J. Courant, Dirac manifolds, Transactions of the American Mathematical Society, 319 (1990), pp. 631–661. M. Gualtieri, Generalized complex geometry, PhD thesis, University of Oxford, 2003. D. Iglesias-Ponte and J. C. Marrero, Lie algebroid foliations and E1(m)-Dirac structures, Journal of Physics A: Mathematical and General, 35 (2002), p. 4085. D. Iglesias-Ponte and A. Wade, Contact manifolds and generalized complex structures, Journal of Geometry and Physics, 53 (2005), pp. 249–258. D. Iglesias-Ponte and A. Wade, Integration of Dirac–Jacobi structures, Journal of Physics A: Mathematical and General, 39 (2006), p. 4181. J. M. Lee, Introduction to smooth manifolds, Graduate Texts in Mathematics, 218 (2003). K. C. Mackenzie and P. Xu, Lie bialgebroids and Poisson groupoids, Duke Math- ematical Journal, 73 (1994), pp. 415–452. M. A. Salazar and D. Sepe, Contact isotropic realisations of Jacobi manifolds via Spencer operators, SIGMA, 13 (2017), p. 033. L. Vitagliano, Dirac–Jacobi bundles, Journal of Symplectic Geometry, 16 (2018), pp. 485–561. A. Wade, Conformal Dirac structures, Letters in Mathematical Physics, 53 (2000), pp. 331–348. A. Weinstein, M. Zambon, C. Molitor-Braun, N. Poncin, and M. Schlichenmaier, Variations on prequantization, Travaux math´ematiques, (2005), pp. 187–219. M. Zambon and C. Zhu, On the geometry of prequantization spaces, Journal of Geometry and Physics, 57 (2007), pp. 2372–2397. C. Zapata-Carratala, Landscape of Hamiltonian phase spaces: on the foundations and generalizations of one of the most powerful ideas of modern science, PhD thesis, The University of Edinburgh, 2019.
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv	Atribución-NoComercial-SinDerivadas 4.0 Internacional
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eu_rights_str_mv	openAccess
dc.format.extent.spa.fl_str_mv	71 páginas
dc.format.mimetype.spa.fl_str_mv	application/pdf
dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ciencias - Maestría en Ciencias - Matemáticas
dc.publisher.department.spa.fl_str_mv	Departamento de Matemáticas
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
bitstream.url.fl_str_mv	https://repositorio.unal.edu.co/bitstream/unal/80403/1/license.txt https://repositorio.unal.edu.co/bitstream/unal/80403/3/1088731960.2021.pdf https://repositorio.unal.edu.co/bitstream/unal/80403/4/1088731960.2021.pdf.jpg
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spelling	Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Martínez Alba, Nicoláse706ea684c96a0e4898ee7ffb47ef9e4Yela Rosero, Darlyn Yamidca18d5b0ddcf9c2d8d1a4d7188ddfe2d2021-10-06T19:34:26Z2021-10-06T19:34:26Z2021-10-04https://repositorio.unal.edu.co/handle/unal/80403Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/In this manuscript we study reductions of Dirac-Jacobi structures on a smooth manifold under the presence of symmetries given by the action of a connected Lie group. The main tools we used are the called "homogenization trick" and the well known reduction of Dirac structures. We show two particular cases, namely, reduction by moment map and the case when the base manifold is endowed with a contact 1-form.En el presente texto se estudia la reducción de estructuras Dirac-Jacobi sobre una variedad diferenciable bajo la presencia de simetrías dadas por la acción de un grupo de Lie conexo. La herramienta principal que se usa es el llamado "truco de homogenización" y las reducciones de Dirac ya conocidas. Se muestran dos casos particulares de reducción Dirac-Jacobi; cuando hay presencia de una aplicación momento y el caso cuando la variedad base está dotada de una 1-forma de contacto. (Texto tomado de la fuente).MaestríaMagíster en Ciencias - MatemáticasGeometría diferencial71 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::516 - GeometríaPhysicsQuantum theoryFísicaTeoría cuánticaDirac-Jacobi structuresDirac structuresDirac-ization trickHomogenization trickReductionEstructuras Dirac-JacobiEstructuras DiracTruco de homogenizaciónTruco de Dirac-izaciónReducciónGeometríaGeometrySymmetries and reductions of Dirac-Jacobi structuresSimetrías y reducciones de estructuras Dirac-JacobiTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMA. A. Belavin and V. G. Drinfeld, Solutions of the classical Yang–Baxter equa- tion for simple Lie algebras, Funktsional’nyi Analiz i ego Prilozheniya, 16 (1982), pp. 1–29.H. Bursztyn, A brief introduction to Dirac manifolds, Geometric and topological methods for quantum field theory, (2013), pp. 4–38.H. Bursztyn, G. R. Cavalcanti, and M. Gualtieri, Reduction of Courant algebroids and generalized complex structures, Advances in Mathematics, 211 (2007), pp. 726–765.J. Costa and F. Petalidou, Twisted Jacobi manifolds, twisted Dirac-Jacobi structures and quasi-Jacobi bialgebroids, Journal of Physics. A, Mathematical and General, 39 (2006).T. J. Courant, Dirac manifolds, Transactions of the American Mathematical Society, 319 (1990), pp. 631–661.M. Gualtieri, Generalized complex geometry, PhD thesis, University of Oxford, 2003.D. Iglesias-Ponte and J. C. Marrero, Lie algebroid foliations and E1(m)-Dirac structures, Journal of Physics A: Mathematical and General, 35 (2002), p. 4085.D. Iglesias-Ponte and A. Wade, Contact manifolds and generalized complex structures, Journal of Geometry and Physics, 53 (2005), pp. 249–258.D. Iglesias-Ponte and A. Wade, Integration of Dirac–Jacobi structures, Journal of Physics A: Mathematical and General, 39 (2006), p. 4181.J. M. Lee, Introduction to smooth manifolds, Graduate Texts in Mathematics, 218 (2003).K. C. Mackenzie and P. Xu, Lie bialgebroids and Poisson groupoids, Duke Math- ematical Journal, 73 (1994), pp. 415–452.M. A. Salazar and D. Sepe, Contact isotropic realisations of Jacobi manifolds via Spencer operators, SIGMA, 13 (2017), p. 033.L. Vitagliano, Dirac–Jacobi bundles, Journal of Symplectic Geometry, 16 (2018), pp. 485–561.A. Wade, Conformal Dirac structures, Letters in Mathematical Physics, 53 (2000), pp. 331–348.A. Weinstein, M. Zambon, C. Molitor-Braun, N. Poncin, and M. Schlichenmaier, Variations on prequantization, Travaux math´ematiques, (2005), pp. 187–219.M. Zambon and C. Zhu, On the geometry of prequantization spaces, Journal of Geometry and Physics, 57 (2007), pp. 2372–2397.C. Zapata-Carratala, Landscape of Hamiltonian phase spaces: on the foundations and generalizations of one of the most powerful ideas of modern science, PhD thesis, The University of Edinburgh, 2019.EstudiantesInvestigadoresMaestrosPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/80403/1/license.txtcccfe52f796b7c63423298c2d3365fc6MD51ORIGINAL1088731960.2021.pdf1088731960.2021.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf550921https://repositorio.unal.edu.co/bitstream/unal/80403/3/1088731960.2021.pdf30d419dc7df1f1bda34a22e2532b9d08MD53THUMBNAIL1088731960.2021.pdf.jpg1088731960.2021.pdf.jpgGenerated Thumbnailimage/jpeg3902https://repositorio.unal.edu.co/bitstream/unal/80403/4/1088731960.2021.pdf.jpgc9a5aea2e60921d7e9613d9bbe00f500MD54unal/80403oai:repositorio.unal.edu.co:unal/804032023-07-29 23:03:42.508Repositorio Institucional Universidad Nacional de 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Symmetries and reductions of Dirac-Jacobi structures

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