Twisted (2+1) κ-AdS algebra, Drinfel'd doubles and non-commutative spacetimes
Ballestreros A, Herranz FJ, Meusburger C, Naranjo P (2014)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2014
Journal
Publisher: National Academy of Science of Ukraine
Book Volume: 10
Abstract
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.
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APA:
Ballestreros, A., Herranz, F.J., Meusburger, C., & Naranjo, P. (2014). Twisted (2+1) κ-AdS algebra, Drinfel'd doubles and non-commutative spacetimes. Symmetry Integrability and Geometry-Methods and Applications, 10. https://dx.doi.org/10.3842/SIGMA.2014.052
MLA:
Ballestreros, Angel, et al. "Twisted (2+1) κ-AdS algebra, Drinfel'd doubles and non-commutative spacetimes." Symmetry Integrability and Geometry-Methods and Applications 10 (2014).
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