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Proposals that quantum gravity gives rise to non-commutative spacetime geometry and deformations of Poincare symmetry are examined in the context of (2+1)-dimensional quantum gravity.
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C. Meusburger and B. J. Schroers, The quantisation of Poisson structures arising in Chern-Simons theory with gauge group G ⋉ 𝔤 ∗ G\ltimes\mathfrak{g}^{*} , Adv. Theor. Math. Phys. 7 (2004) 1003–1043
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C. Meusburger and B. J. Schroers, Quaternionic and Poisson-Lie structures in 3d gravity: the cosmological constant as deformation parameter, arXive:0708.1507
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S. Majid and B. Schroers, q-deformation and semidualisation in 2+1 quantum gravity, in preparation
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G. Amelino-Camelia, L. Smolin and A. Starodubtsev, Quantum symmetry, the cosmological constant and Planck scale phenomenology, Class. Quant. Grav. 21 (2004) 3095–3110
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J. Kowalski-Glikman, Introduction to doubly special relativity, Lect. Notes Phys. 669 (2005) 131–159; also hep-th/0405273
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K. Noui, Three dimensional loop quantum gravity: towards a self-gravitating quantum field theory, Class. Quant. Grav. 24 (2007) 329–360
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