QUANTUM POINCARE GROUP WITHOUT DILATATION AND TWISTED CLASSICAL ALGEBRA

A quantum deformation of a Poincaré group was constructed using as a starting point SU(2,2) conformal group and twistorlike definition of the Minkowski space. This leads to a pure twisted quantum Poincaré group. The relative simplicity of the q deformation permits one to find out the important properties of the q groups of the space-time transformations. In particular, it is shown that the geometrical meaning of the twisting is the transition to the another space-time coordinates frame, so that one can freely choose the most convenient deformation among the ones related to each other by twists. The small subgroup used in the induced representation construction is proven to be twisted with respect to initial q group. This last fact means that commutation relations for creation and destruction operators are not strongly defined by the q group of the space-time transformations. © 1995 American Institute of Physics.