{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T22:01:00Z","timestamp":1782338460478,"version":"3.54.5"},"reference-count":129,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,5]],"date-time":"2021-11-05T00:00:00Z","timestamp":1636070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministerio de Ciencia e Innovaci\u00f3n, Spain","award":["MTM2016-79639-P (AEI\/FEDER, UE)"],"award-info":[{"award-number":["MTM2016-79639-P (AEI\/FEDER, UE)"]}]},{"name":"Ministerio de Ciencia e Innovaci\u00f3n, Spain","award":["PID2019 - 106802GB-I00 \/ AEI \/ 10.13039 \/ 501100011033"],"award-info":[{"award-number":["PID2019 - 106802GB-I00 \/ AEI \/ 10.13039 \/ 501100011033"]}]},{"name":"Junta de Castilla y Le\u00f3n, Spain","award":["BU229P18"],"award-info":[{"award-number":["BU229P18"]}]},{"name":"Junta de Castilla y Le\u00f3n, Spain","award":["GIR2019"],"award-info":[{"award-number":["GIR2019"]}]},{"DOI":"10.13039\/501100000921","name":"European Cooperation in Science and Technology","doi-asserted-by":"publisher","award":["COST Action CA18108 QG-MM"],"award-info":[{"award-number":["COST Action CA18108 QG-MM"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recent work showed that \u03ba-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincar\u00e9 algebra of special-relativistic symmetries, one can toggle the curvature parameter \u039b, the Planck scale quantum deformation parameter \u03ba and the speed of light parameter c to move to the well-studied \u03ba-Poincar\u00e9 algebra, the (quantum) (A)dS algebra, the (quantum) Galilei and Carroll algebras and their curved versions. In this review, we survey the properties and relations of these algebras of relativistic symmetries and their associated noncommutative spacetimes, emphasizing the nontrivial effects of interplay between curvature, quantum deformation and speed of light parameters.<\/jats:p>","DOI":"10.3390\/sym13112099","type":"journal-article","created":{"date-parts":[[2021,11,7]],"date-time":"2021-11-07T20:42:54Z","timestamp":1636317774000},"page":"2099","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Interplay between Spacetime Curvature, Speed of Light and Quantum Deformations of Relativistic Symmetries"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4085-3094","authenticated-orcid":false,"given":"Angel","family":"Ballesteros","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Burgos, 09001 Burgos, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giulia","family":"Gubitosi","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica \u201cEttore Pancini\u201d, Universit\u00e0 di Napoli Federico II, 80126 Napoli, Italy"},{"name":"National Institute of Nuclear Physics,  Sezione di Napoli, 80126 Napoli, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Flavio","family":"Mercati","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Burgos, 09001 Burgos, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"084010","DOI":"10.1103\/PhysRevD.84.084010","article-title":"The principle of relative locality","volume":"84","author":"Freidel","year":"2011","journal-title":"Phys. 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