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@article{faucris.122162304,
abstract = {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.},
author = {Ballesteros, Angel and Herranz, Francisco J. and Meusburger, CathÃ©rine},
doi = {10.1088/0264-9381/30/15/155012},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Drinfel}'d doubles for (2+1)-gravity},
volume = {30},
year = {2013}
}