A new quantum so(2,2) algebra

Abstract

By starting from the non-standard quantum deformation of the sl(2,R) algebra, a new quantum deformation for the real Lie algebra so(2,2) is constructed by imposing the former to be a Hopf subalgebra of the latter. The quantum so(2,2) algebra so obtained is realized as a quantum conformal algebra of the (1+1) Minkowskian spacetime. This Hopf algebra is shown to be the symmetry algebra of a time discretization of the (1+1) wave equation and its contraction gives rise to a new $(2+1)$ quantum Poincaré algebra.

arXiv comment5 pages, LaTeX. Contribution to the Procs. Quantum Theory and Symmetries (Goslar, 18-22 July 1999) (World Scientific, 2000), edited by H.-D. Doebner, V.K. Dobrev, J.-D. Hennig and W. Luecke