Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes

Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes

We construct the full quantum algebra, the corresponding Poisson-Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)-dimensional anti-de Sitter (AdS), de Sitter (dS) and Minkowski spaces. These deformations correspond to a Dri...

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Бібліографічні деталі
Дата:2014
Автори: Ballesteros, A., Herranz, F.J., Meusburger, C., Naranjo, P.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2014
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/146687
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes / A. Ballesteros, F.J. Herranz, C. Meusburger, P. Naranjo // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-146687
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spelling irk-123456789-1466872019-02-11T01:25:10Z Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes Ballesteros, A. Herranz, F.J. Meusburger, C. Naranjo, P. We construct the full quantum algebra, the corresponding Poisson-Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)-dimensional anti-de Sitter (AdS), de Sitter (dS) and Minkowski spaces. These deformations correspond to a Drinfel'd double structure on the isometry algebras that are motivated by their role in (2+1)-gravity. The construction includes the cosmological constant Λ as a deformation parameter, which allows one to treat these cases in a common framework and to obtain a twisted version of both space- and time-like κ-AdS and dS quantum algebras; their flat limit Λ→0 leads to a twisted quantum Poincaré algebra. The resulting non-commutative spacetime is a nonlinear Λ-deformation of the κ-Minkowski one plus an additional contribution generated by the twist. For the AdS case, we relate this quantum deformation to two copies of the standard (Drinfel'd-Jimbo) quantum deformation of the Lorentz group in three dimensions, which allows one to determine the impact of the twist. 2014 Article Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes / A. Ballesteros, F.J. Herranz, C. Meusburger, P. Naranjo // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16T20; 81R50; 81R60 DOI:10.3842/SIGMA.2014.052 http://dspace.nbuv.gov.ua/handle/123456789/146687 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description We construct the full quantum algebra, the corresponding Poisson-Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)-dimensional anti-de Sitter (AdS), de Sitter (dS) and Minkowski spaces. These deformations correspond to a Drinfel'd double structure on the isometry algebras that are motivated by their role in (2+1)-gravity. The construction includes the cosmological constant Λ as a deformation parameter, which allows one to treat these cases in a common framework and to obtain a twisted version of both space- and time-like κ-AdS and dS quantum algebras; their flat limit Λ→0 leads to a twisted quantum Poincaré algebra. The resulting non-commutative spacetime is a nonlinear Λ-deformation of the κ-Minkowski one plus an additional contribution generated by the twist. For the AdS case, we relate this quantum deformation to two copies of the standard (Drinfel'd-Jimbo) quantum deformation of the Lorentz group in three dimensions, which allows one to determine the impact of the twist.
format Article
author Ballesteros, A.
Herranz, F.J.
Meusburger, C.
Naranjo, P.
spellingShingle Ballesteros, A.
Herranz, F.J.
Meusburger, C.
Naranjo, P.
Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Ballesteros, A.
Herranz, F.J.
Meusburger, C.
Naranjo, P.
author_sort Ballesteros, A.
title Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
title_short Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
title_full Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
title_fullStr Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
title_full_unstemmed Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
title_sort twisted (2+1) κ-ads algebra, drinfel'd doubles and non-commutative spacetimes
publisher Інститут математики НАН України
publishDate 2014
url http://dspace.nbuv.gov.ua/handle/123456789/146687
citation_txt Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes / A. Ballesteros, F.J. Herranz, C. Meusburger, P. Naranjo // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 65 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
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AT naranjop twisted21kadsalgebradrinfelddoublesandnoncommutativespacetimes
first_indexed 2023-05-20T17:25:25Z
last_indexed 2023-05-20T17:25:25Z
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