On the classification of quantum Poincaré groups

Abstract

Using the general theory of [10] ( hep-th 9412058 ), quantum Poincaré groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most cases we solve them and give the classification of quantum Poincaré groups. Each of them corresponds to exactly one quantum Minkowski space. The Poincaré series of these objects are the same as in the classical case. We also classify possible $R$-matrices for the fundamental representation of the group.