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A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant (1402.2884v2)
Published 12 Feb 2014 in math-ph, gr-qc, hep-th, and math.MP
Abstract: 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 $\Lambda=-\eta2$. 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 $\Lambda\neq 0$ are sketched, and it is shown that the new non-commutative AdS spacetime is a nonlinear $\Lambda$-deformation of the Minkowskian one.