Abstract
With a view towards applications for de Sitter, we construct the multiparametric
Research Article | Open Access
Multiparametric Quantum Algebras and the Cosmological Constant
Academic Editor: P. H. Frampton
Received17 Jul 2007
Accepted26 Sept 2007
Published15 Nov 2007
References
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.
View at: Google ScholarT. Banks, “Cosmological breaking of supersymmetry?” International Journal of Modern Physics A, vol. 16, no. 5, pp. 910–921, 2001.
View at: Google ScholarR. Bousso, “Positive vacuum energy and the -bound,” Journal of High Energy Physics, vol. 11, no. 38, 25 pages, 2000.
View at: Publisher Site | Google ScholarW. 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.
View at: Publisher Site | Google ScholarP. 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.
View at: Publisher Site | Google ScholarA. 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.
View at: Publisher Site | Google ScholarA. 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.
View at: Publisher Site | Google ScholarD. A. Lowe, “-deformed de Sitter/conformal field theory correspondence,” Physical Review D, vol. 70, no. 10, Article ID 104002, 7 pages, 2004.
View at: Publisher Site | Google ScholarH. Steinacker, “Unitary representations of noncompact quantum groups at roots of unity,” Reviews in Mathematical Physics (RMP), vol. 13, no. 8, pp. 1035–1054, 2001.
View at: Publisher Site | Google ScholarH. Steinacker, “Quantum groups, roots of unity and particles on quantized anti-de Sitter space,” preprint, 1997, http://arxiv.org/abs/hep-th/9705211.
View at: Google ScholarH. 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.
View at: Publisher Site | Google ScholarC. 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.
View at: Publisher Site | Google ScholarN. 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.
View at: Google ScholarN. Yu. Reshetikhin, “Multiparameter quantum groups and twisted quasitriangular Hopf algebras,” Letters in Mathematical Physics, vol. 20, no. 4, pp. 331–335, 1990.
View at: Publisher Site | Google ScholarA Schirrmacher, “Multiparameter R-matrices and their quantum groups,” Journal of Physics A, vol. 24, no. 21, pp. L1249–L1258, 1991.
View at: Publisher Site | Google ScholarM. 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.
View at: Google ScholarM. 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.
View at: Publisher Site | Google ScholarA. 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.
View at: Google ScholarS. 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.
View at: Publisher Site | Google ScholarA. 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/.
View at: Google Scholar
Copyright
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.