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Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Twisted (2+1) κ-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
Інший ID:
2010 Mathematics Subject Classification: 16T20; 81R50; 81R60
DOI:10.3842/SIGMA.2014.052
DOI:10.3842/SIGMA.2014.052
Посилання:
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.
Підтримка:
This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
full collection is available at http://www.emis.de/journals/SIGMA/space-time.html.
This work was partially supported by the Spanish MICINN under grant MTM2010-18556 and by
the DFG Emmy-Noether fellowship ME 3425/1-2. P.N. acknowledges a postdoctoral fellowship
from Junta de Castilla y Le´on (Spain).
Дата:
2014
Переглядів:
491
Завантажень:
253
Анотація:
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.
