Drinfel%26apos;d doubles for (2+1)-gravity

作者：Ballesteros Angel^*; Herranz Francisco J; Meu**urger Catherine

来源：Classical and Quantum Gravity, 2013, 30(15): 155012.

DOI：10.1088/0264-9381/30/15/155012

All possible Drinfel%26apos;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%26apos;d double structure for the Poincare algebra iso(2, 1) in the limit when the cosmological constant tends to zero. We explain how these Drinfel%26apos;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.

• 出版日期2013-8-7