A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant

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

来源：Physics Letters B, 2014, 732: 201-209.

DOI：10.1016/j.physletb.2014.03.036

• (2+1) gravity
• Non-commutative spacetime
• Anti de Sitter
• Cosmological constant
• Quantum groups
• Poisson Lie groups

We show that the Drinfel'd double associated to the standard quantum deformation sl(eta)(2, R) is isomorphic to the (2 + 1)-dimensional AdS algebra with the initial deformation parameter eta related to the cosmological constant Lambda = -eta(2). This gives rise to a generalisation of a non-commutative Minkowski spacetime that arises as a consequence of the quantum double symmetry of (2 + 1) gravity to non-vanishing cosmological constant. The properties of the AdS quantum double that generalises this symmetry to the case Lambda not equal 0 are sketched, and it is shown that the new non-commutative AdS spacetime is a nonlinear Lambda-deformation of the Minkowskian one.

• 出版日期2014-5-1