Quantum deformations of conformal algebras with mass-like deformation parameters

Details Quantum deformations of conformal algebras with mass-like deformation parameters Quantum deformations of conformal algebras with mass-like deformation parameters

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998aipc..453...53f&link_type=abstract

Particles, fields and gravitation. AIP Conference Proceedings, Volume 453, pp. 53-66 (1998).

Mathematics

1

Theory Of Quantized Fields, Field Theory, Algebraic Methods

Scientific paper

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), Fröbenius 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)~=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.

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