Three-dimensional gravity and Drinfel'd doubles: Spacetimes and symmetries from quantum deformations

Journal article
(Original article)


Publication Details

Author(s): Ballestreros A, Herranz FJ, Meusburger C
Journal: Physics Letters B
Publisher: Elsevier
Publication year: 2010
Volume: 687
Pages range: 375-381
ISSN: 0370-2693


Abstract


We show how the constant curvature spacetimes of 3d gravity and the associated symmetry algebras can be derived from a single quantum deformation of the 3d Lorentz algebra sl (2, R). We investigate the classical Drinfel'd double of a "hybrid" deformation of sl (2, R) that depends on two parameters (η, z). With an appropriate choice of basis and real structure, this Drinfel'd double agrees with the 3d anti-de Sitter algebra. The deformation parameter η is related to the cosmological constant, while z is identified with the inverse of the speed of light and defines the signature of the metric. We generalise this result to de Sitter space, the three-sphere and 3d hyperbolic space through analytic continuation in η and z; we also investigate the limits of vanishing η and z, which yield the flat spacetimes (Minkowski and Euclidean spaces) and Newtonian models, respectively. © 2010 Elsevier B.V. All rights reserved.



FAU Authors / FAU Editors

Meusburger, Cathérine Prof.
Professur für Mathematik (Darstellungstheorie und Mathematische Physik)


How to cite

APA:
Ballestreros, A., Herranz, F.J., & Meusburger, C. (2010). Three-dimensional gravity and Drinfel'd doubles: Spacetimes and symmetries from quantum deformations. Physics Letters B, 687, 375-381. https://dx.doi.org/10.1016/j.physletb.2010.03.043

MLA:
Ballestreros, Angel, Francisco J. Herranz, and Cathérine Meusburger. "Three-dimensional gravity and Drinfel'd doubles: Spacetimes and symmetries from quantum deformations." Physics Letters B 687 (2010): 375-381.

BibTeX: 

Last updated on 2018-22-10 at 21:50