ON THE CLASSIFICATION OF QUANTUM POINCARE GROUPS

Using the general theory of [10], quantum Poincare groups (without dil atations) are described and investigated. The description contains a s et of numerical parameters which satisfy certain polynomial equations. For most cases we solve them and give the classification of quantum P oincare groups. Each of them corresponds to exactly one quantum Minkow ski space. The Poincare series of these objects are the same as in the classical case. We also classify possible R-matrices for the fundamen tal representation of the group.