Approaches to Quantum Gravity

492 S. Majid[4] S. Majid and L. Freidel, Noncommutative harmonic analysis, sampling theory andthe Duflo map in 2+1 quantum gravity, Class. Quant. Gravity, 25 (2008) 045006,hep-th/0601004.[5] A. Kempf and S. Majid, Algebraic q-integration and Fourier theory on quantum andbraided spaces, J. Math. Phys. 35 (1994) 6802–6837.[6] V. Lyubashenko and S. Majid, Braided groups and quantum Fourier transform, J.Algebra 166 (1994) 506–528.[7] V. Lyubashenko and S. Majid, Fourier transform identities in quantum mechanicsand the quantum line, Phys. Lett. B 284 (1992) 66–70.[8] J. Lukierski, A. Nowicki, H. Ruegg and V. N. Tolstoy, q-Deformation of Poincaréalgebra, Phys. Lett. B. 268 (1991) 331–338.[9] S. Majid. Duality principle and braided geometry, in Springer Lect. Notes Phys., 447(1995) 125–144.[10] S. Majid, Foundations of Quantum Group Theory (Cambridge University Press,1995).[11] S. Majid, Algebraic approach to quantum gravity III: quantum Riemanniangeometry, in Mathematical and Physical Aspects of Quantum Gravity, B. Fauser andJ. Tolksdorf, eds. (Birkhauser, 2006), pp. 77–100, hep-th/0604132.[12] S. Majid, Noncommutative-geometric Groups by a Bicrossproduct Construction,(Ph.D. thesis, Harvard mathematical physics, 1988).[13] S. Majid, Hopf algebras for physics at the Planck scale, J. Classical and QuantumGravity, 5 (1988) 1587–1606.[14] S. Majid, Physics for algebraists: noncommutative and noncocommutative Hopfalgebras by a bicrossproduct construction, J. Algebra 130 (1990) 17–64.[15] S. Majid, Matched pairs of Lie groups associated to solutions of the Yang–Baxterequations, Pac. J. Math. 141 (1990) 311–332.[16] S. Majid, Hopf–von Neumann algebra bicrossproducts, Kac algebra bicrossproducts,and the classical Yang–Baxter equations, J. Funct. Analysis 95 (1991) 291–319.[17] S. Majid, The principle of representation-theoretic self-duality, Phys. Essays 4(1991) 395–405.[18] S. Majid, Tannaka–Krein theorem for quasiHopf algebras and other results,Contemp. Math. 134 (1992) 219–232.[19] S. Majid, Examples of braided groups and braided matrices, J. Math. Phys. 32(1991) 3246–3253.[20] S. Majid, Braided momentum in the q-Poincaré group, J. Math. Phys. 34 (1993)2045–2058.[21] S. Majid, Noncommutative model with spontaneous time generation and Planckianbound, J. Math. Phys. 46 (2005) 103520.[22] S. Majid and R. Oeckl, Twisting of quantum differentials and the Planck scale Hopfalgebra, Commun. Math. Phys. 205 (1999) 617–655.[23] S. Majid and H. Ruegg, Bicrossproduct structure of the κ-Poincaré group andnon-commutative geometry, Phys. Lett. B 334 (1994) 348–354.[24] P. Podles and S. L. Woronowicz, On the classification of quantum Poincaré groups,Comm. Math. Phys. 178 (1996) 6182.[25] S.L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantumgroups), Comm. Math. Phys. 122 (1989) 125–170.