Quantum deformations of conformal algebras with mass-like deformation parameters
- Institute for Theoretical Physics, University of Wroclaw, 50-204 Wroclaw (Poland)
- Laboratoire de Physique Theorique, Universite Bordeaux 1, 33-175 Gradignan (France)
We recall the mathematical apparatus necessary for the quantum deformation of Lie algebras, namely the notions of coboundary Lie algebras, classical r-matrices, classical Yang-Baxter equations (CYBE), Froebenius algebras and parabolic subalgebras. Then we construct the quantum deformation of D=1, D=2 and D=3 conformal algebras, showing that this quantization introduce fundamental mass parameters. Finally we consider with more details the quantization of D=4 conformal algebra. We build three classes of sl(4,C) classical r-matrices, satisfying CYBE and depending respectively on 8, 10 and 12 generators of parabolic subalgebras. We show that only the 8-dimensional r-matrices allow to impose the D=4 conformal o(4,2){approx_equal}su(2,2) reality conditions. Weyl reflections and Dynkin diagram automorphisms for o(4,2) define the class of admissible bases for given classical r-matrices.
- OSTI ID:
- 21202687
- Journal Information:
- AIP Conference Proceedings, Vol. 453, Issue 1; Conference: Conference on particles, fields and gravitation, Lodz (Poland), 15-19 Apr 1998; Other Information: DOI: 10.1063/1.57114; (c) 1998 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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