Research Article | Open Access
Chethan Krishnan, Edoardo Di Napoli, "Multiparametric Quantum Algebras and the Cosmological Constant", Advances in High Energy Physics, vol. 2007, Article ID 013458, 10 pages, 2007. https://doi.org/10.1155/2007/13458
Multiparametric Quantum Algebras and the Cosmological Constant
With a view towards applications for de Sitter, we construct the multiparametric -deformation of the so algebra using the Faddeev-Reshetikhin-Takhtadzhyan (FRT) formalism.
- W. Fischler, “Taking de Sitter seriously,” Talk given at The Role of Scaling Laws in Physics and Biology (Celebrating the 60th birthday of Geoffrey West), Santa Fe, December 200.
- T. Banks, “Cosmological breaking of supersymmetry?” International Journal of Modern Physics A, vol. 16, no. 5, pp. 910–921, 2001.
- R. Bousso, “Positive vacuum energy and the -bound,” Journal of High Energy Physics, vol. 11, no. 38, 25 pages, 2000.
- W. Fischler, A. Kashani-Poor, R. McNees, and S. Paban, “The acceleration of the universe, a challenge for string theory,” Journal of High Energy Physics, vol. 7, no. 3, 12 pages, 2001.
- P. Pouliot, “Finite number of states, de Sitter space and quantum groups at roots of unity,” Classical and Quantum Gravity, vol. 21, no. 1, pp. 145–162, 2004.
- A. Güijosa and D. A. Lowe, “New twist on the dS/CFT correspondence,” Physical Review D, vol. 69, no. 10, Article ID 106008, 9 pages, 2004.
- A. Güijosa, D. A. Lowe, and J. Murugan, “Prototype for dS/CFT correspondence,” Physical Review D, vol. 72, no. 4, Article ID 046001, 7 pages, 2005.
- D. A. Lowe, “-deformed de Sitter/conformal field theory correspondence,” Physical Review D, vol. 70, no. 10, Article ID 104002, 7 pages, 2004.
- H. Steinacker, “Unitary representations of noncompact quantum groups at roots of unity,” Reviews in Mathematical Physics (RMP), vol. 13, no. 8, pp. 1035–1054, 2001.
- H. Steinacker, “Quantum groups, roots of unity and particles on quantized anti-de Sitter space,” preprint, 1997, http://arxiv.org/abs/hep-th/9705211.
- H. Steinacker, “Finite dimensional unitary representations of quantum anti-de Sitter groups at roots of unity,” Communications in Mathematical Physics, vol. 192, no. 3, pp. 687–706, 1998.
- C. Krishnan and E. di Napoli, “Can quantum de Sitter space have finite entropy?” Classical and Quantum Gravity, vol. 24, no. 13, pp. 3457–3463, 2007.
- N. Yu. Reshetikhin, L. A. Takhtadzhyan, and L. D. Faddeev, “Quantization of Lie groups and Lie algebras,” Leningrad Mathematical Journal, vol. 1, no. 1, pp. 193–225, 1990.
- N. Yu. Reshetikhin, “Multiparameter quantum groups and twisted quasitriangular Hopf algebras,” Letters in Mathematical Physics, vol. 20, no. 4, pp. 331–335, 1990.
- A Schirrmacher, “Multiparameter R-matrices and their quantum groups,” Journal of Physics A, vol. 24, no. 21, pp. L1249–L1258, 1991.
- M. K. Parikh and E. P. Verlinde, “de Sitter space with finitely many states: a toy story,” based in part on a talk given at the 10th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG X MMIII), Rio de Janeiro, Brazil, 200.
- M. K. Parikh and E. P. Verlinde, “de Sitter holography with a finite number of states,” Journal of High Energy Physics, vol. 1, no. 54, 21 pages, 2005.
- A. Jevicki, M. Mihailescu, and S. Ramgoolam, “Hidden classical symmetry in quantum spaces at roots of unity : from q-sphere to fuzzy sphere,” preprint, 2000, http://arxiv.org/abs/hep-th/0008186.
- S. Corley and S. Ramgoolam, “Strings on plane waves, super-Yang-Mills in four dimensions, quantum groups at roots of one,” Nuclear Physics B, vol. 676, no. 1-2, pp. 99–128, 2004.
- A. Klimyk and K. Schmudgen, Quantum Groups and Their Representations, Springer, Berlin, Germany, 1997.
- R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Benjamin/Cummings, San Francisco, Calif, USA, 1984.
- J. W. Helton and R. L. Miller, “NCAlgebra version 3.7,” http://www.math.ucsd.edu/~ncalg/.
Copyright © 2007 Chethan Krishnan and Edoardo Di Napoli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.