4-DIMENSIONAL QUANTUM AFFINE ALGEBRAS AND SPACE-TIME Q-SYMMETRIES

A global model of the q deformation for the quasiorthogonal Lie algebr as generating the groups of motions of the four-dimensional affine Cay ley-Klein (CK) geometries is obtained starting from the three-dimensio nal deformations. It is shown how the main algebraic classical propert ies of the CK systems can be implemented in the quantum case. Quantum deformed versions either of the space-time or space symmetry algebras [Poincare (3+1), Galilei (3+1), 4-D Euclidean as well as others] appea r in this context as particular cases. For some of these classical alg ebras several q deformations are directly obtained.