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Эта публикация цитируется в 21 научных статьях (всего в 21 статьях)
Twisted (2+1) $\kappa$-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
Ángel Ballesterosa, Francisco J. Herranza, Catherine Meusburgerb, Pedro Naranjoa a Departamento de Física, Universidad de Burgos, E-09001 Burgos, Spain
b Department Mathematik, Friedrich-Alexander University of Erlangen-Nürnberg, Cauerstr. 11, D-91058 Erlangen, Germany
Аннотация:
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 $\Lambda$ 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 $\kappa$-AdS and dS quantum algebras; their flat limit $\Lambda\to 0$ leads to a twisted quantum Poincaré algebra. The resulting non-commutative spacetime is a nonlinear $\Lambda$-deformation of the $\kappa$-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.
Ключевые слова:
(2+1)-gravity; deformation; non-commutative spacetime; anti-de Sitter; cosmological constant; quantum groups;
Poisson–Lie groups; contraction.
Поступила: 9 марта 2014 г.; в окончательном варианте 13 мая 2014 г.; опубликована 18 мая 2014 г.
Образец цитирования:
Ángel Ballesteros, Francisco J. Herranz, Catherine Meusburger, Pedro Naranjo, “Twisted (2+1) $\kappa$-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes”, SIGMA, 10 (2014), 052, 26 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma917 https://www.mathnet.ru/rus/sigma/v10/p52
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