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Generalized noncommutative Snyder spaces and projective geometry Gubitosi, Giulia Ballesteros Castañeda, Ángel Herranz Zorrilla, Francisco José Física Physics Trabajo presentado en: Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019) - Workshop on Quantum Geometry, Field Theory and Gravity, 31 August - 25 September, Corfù, Greece Given a group of kinematical symmetry generators, one can construct a compatible noncommutative spacetime and deformed phase space by means of projective geometry. This was the main idea behind the very first model of noncommutative spacetime, proposed by H.S. Snyder in 1947. In this framework, spacetime coordinates are the translation generators over a manifold that is symmetric under the required generators, while momenta are projective coordinates on such a manifold. In these proceedings we review the construction of Euclidean and Lorentzian noncommutative Snyder spaces and investigate the freedom left by this construction in the choice of the physical momenta, because of different available choices of projective coordinates. In particular, we derive a quasi-canonical structure for both the Euclidean and Lorentzian Snyder noncommutative models such that their phase space algebra is diagonal although no longer quadratic. This work has been partially supported by Ministerio de Ciencia, Innovación y Universidades (Spain) under grant MTM2016-79639-P (AEI/FEDER, UE), by Junta de Castilla y León (Spain) under grants BU229P18 and BU091G19. The authors acknowledge the contribution of the COST Action CA18108. 2023-01-09T11:55:21Z 2023-01-09T11:55:21Z 2020-08 info:eu-repo/semantics/conferenceObject info:eu-repo/semantics/publishedVersion 1824-8039 http://hdl.handle.net/10259/7222 10.22323/1.376.0190 eng Proceedings of Science. 2020, V. 376, p. 190-205 https://doi.org/10.22323/1.376.0190 info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-79639-P/ES/GRUPOS CUANTICOS, ALGEBRAS DE POISSON Y SISTEMAS INTEGRABLES info:eu-repo/grantAgreement/Junta de Castilla y León//BU229P18//Modelización matemática en tecnologías cuánticas y nanomateriales info:eu-repo/grantAgreement/Junta de Castilla y León//BU091G19//Grupos cuánticos, modelos integrables y aplicaciones en tecnologías cuánticas info:eu-repo/grantAgreement/COST//CA18108/EU/Quantum gravity phenomenology in the multi-messenger approach/QG-MM/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess application/pdf Sissa https://riubu.ubu.es/bitstream/10259/7222/4/Herranz-pos_2020.pdf.jpg Hispana TEXT http://creativecommons.org/licenses/by-nc-nd/4.0/ RIUBU. Repositorio Institucional de la Universidad de Burgos http://hdl.handle.net/10259/7222