Crystallographic classes on the Minkowski space R 1,2. II. Tables of groups

Abstract

For the Minkowski spaces, the traditional definition of a crystallographic group yields only trivial groups that are isomorphic to the Euclidean groups. In this article, we use a weaker definition (the topological discreteness). We classify the isomorphism types of the groups in the six crystallographic classes in the 3-dimensional Minkowski space: three classes are determined by the unimodular subgroups of the general Lorentz group, and the other three classes, by the subgroups unimodular in isotropic coordinates.