Drinfel'd doubles for (2+1)-gravity

Journal article
(Original article)

Publication Details

Author(s): Ballesteros A, Herranz FJ, Meusburger C
Journal: Classical and Quantum Gravity
Publisher: Institute of Physics: Hybrid Open Access
Publication year: 2013
Volume: 30
Journal issue: 15
ISSN: 0264-9381


All possible Drinfel'd double structures for the anti-de Sitter Lie algebra so(2, 2) and de Sitter Lie algebra so(3, 1) in (2+1)-dimensions are explicitly constructed and analysed in terms of a kinematical basis adapted to (2+1)-gravity. Each of these structures provides in a canonical way a pairing among the (anti-)de Sitter generators, as well as a specific classical r-matrix, and the cosmological constant is included in them as a deformation parameter. It is shown that four of these structures give rise to a Drinfel'd double structure for the Poincaré algebra iso(2, 1) in the limit when the cosmological constant tends to zero. We explain how these Drinfel'd double structures are adapted to (2+1)-gravity, and we show that the associated quantum groups are natural candidates for the quantum group symmetries of quantized (2+1)-gravity models and their associated non-commutative spacetimes. © 2013 IOP Publishing Ltd.

FAU Authors / FAU Editors

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

External institutions with authors

University of Burgos / Universidad de Burgos (UBU)

How to cite

Ballesteros, A., Herranz, F.J., & Meusburger, C. (2013). Drinfel'd doubles for (2+1)-gravity. Classical and Quantum Gravity, 30(15). https://dx.doi.org/10.1088/0264-9381/30/15/155012

Ballesteros, Angel, Francisco J. Herranz, and Cathérine Meusburger. "Drinfel'd doubles for (2+1)-gravity." Classical and Quantum Gravity 30.15 (2013).


Last updated on 2018-16-10 at 21:50