RT info:eu-repo/semantics/article
T1 AdS Poisson homogeneous spaces and Drinfel’d doubles
A1 Ballesteros Castañeda, Ángel
A1 Meusburger, Catherine
A1 Naranjo, Pedro
AB The correspondence between Poisson homogeneous spaces over a Poisson-Lie group G andLagrangian Lie subalgebras of the classical double D(g) is revisited and explored in detail for the case in which g = D(a) is a classical double itself. We apply these results to give an explicit description of some coisotropic 2d Poisson homogeneous spaces over the group SL(2,R) ∼= SO(2, 1), namely 2d anti de Sitter space, 2d hyperbolic space and the lightcone in 3d Minkowski space. We show how each of these spaces is obtained as a quotient with respect to a Poisson-subgroup for one of the three inequivalent Lie bialgebra structures on sl(2,R) and as a coisotropic one for the others.We then construct families of coisotropic Poisson homogeneous structures for 3d anti de Sitterspace AdS3 and show that the ones that are quotients by a Poisson subgroup are determined by a three-parameter family of classical r-matrices for so(2, 2), while the non Poisson-subgroup cases are much more numerous. In particular, we present the two Poisson homogeneous structures on AdS3 that arise from two Drinfel’d double structures on SO(2, 2). The first one realises AdS3 as a quotient of SO(2, 2) by the Poisson-subgroup SL(2,R), while the second one, the non-commutative spacetime of the twisted κ-AdS deformation, realises AdS3 as a coisotropic Poisson homogeneous space.
YR 2017
FD 2017
LK http://uvadoc.uva.es/handle/10324/33638
UL http://uvadoc.uva.es/handle/10324/33638
LA eng
NO Journal of Physics A: Mathematical and Theoretical, vol. 50 (2017) 395202
NO Producción Científica
DS UVaDOC
RD 22-nov-2024