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oai:riubu.ubu.es:10259/47302022-12-20T11:45:35Zcom_10259.4_2557com_10259_5086com_10259_2604col_10259.4_2558

Ballesteros Castañeda, Ángel 46 500 0000-0003-4085-3094 Bruno, N. Rossano 78 600 Herranz Zorrilla, Francisco José 280 500 0000-0002-5323-616X 2018-02-06T08:15:38Z 2018-02-06T08:15:38Z 2017 1687-7357 http://hdl.handle.net/10259/4730 10.1155/2017/7876942 The -deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel’d-double and the Poisson–Lie structure underlying the -deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson–Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize the -Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of “duality” between the cosmological constant and the Planck scale is also envisaged. Ministerio de Econom´ıa y Competitividad (MINECO, Spain) under Grants MTM2013-43820-P and MTM2016-79639-P (AEI/FEDER, UE), by Junta de Castilla y Le´on (Spain) under Grants BU278U14 and VA057U16, and by the Action MP1405 QSPACE from the European Cooperation in Science and Technology (COST) application/pdf eng Hindawi Publishing Corporation Advances in High Energy Physics. 2017, V. 2017, art. ID 7876942 https://doi.org/10.1155/2017/7876942 info:eu-repo/grantAgreement/MINECO/MTM2013-43820-P info:eu-repo/grantAgreement/MINECO/MTM2016-79639-P info:eu-repo/grantAgreement/JCyL/BU278U14 info:eu-repo/grantAgreement/JCyL/VA057U16 info:eu-repo/grantAgreement/UE/COST-MP1405 Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Physics Física Noncommutative relativistic spacetimes and worldlines from 2 + 1 quantum (Anti-)de sitter groups info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion CC-LICENSE license_rdf license_rdf application/rdf+xml; charset=utf-8 908 https://riubu.ubu.es/bitstream/10259/4730/8/license_rdf 0175ea4a2d4caec4bbcc37e300941108 MD5 8 THUMBNAIL Ballesteros-AHEP_2017.pdf.jpg Ballesteros-AHEP_2017.pdf.jpg IM Thumbnail image/jpeg 3107 https://riubu.ubu.es/bitstream/10259/4730/7/Ballesteros-AHEP_2017.pdf.jpg 7d0ee927a010b6285391535bc012f418 MD5 7 ORIGINAL Ballesteros-AHEP_2017.pdf Ballesteros-AHEP_2017.pdf application/pdf 1651425 https://riubu.ubu.es/bitstream/10259/4730/1/Ballesteros-AHEP_2017.pdf 3edb4ecbb8bb58b361dfbf0b3fd1da72 MD5 1 LICENSE license.txt license.txt text/plain; charset=utf-8 998 https://riubu.ubu.es/bitstream/10259/4730/5/license.txt aa90105e1c90a1b4fe810649aa967b7d MD5 5 TEXT Ballesteros-AHEP_2017.pdf.txt Ballesteros-AHEP_2017.pdf.txt Extracted text text/plain 92505 https://riubu.ubu.es/bitstream/10259/4730/6/Ballesteros-AHEP_2017.pdf.txt 1b679e3b04dd6a39adae45a142a5e479 MD5 6 10259/4730 oai:riubu.ubu.es:10259/4730 2022-12-20 12:45:35.121 Repositorio Institucional de la Universidad de Burgos bubrep@ubu.es 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