On Some Discrete Subgroups of The Lorentz Group

Abstract

Some discrete subgroups of the Lorentz group are found using Fedorov’s parametrization by means of complex vector-parameter. It is shown that the discrete subgroup of the Lorentz group, which have not fixed points, are contained in boosts along a spatial direction for time-like and space-like vectors and are discrete subgroups of the group SO(1, 1), whereas discrete subgroups of isotropic vector are subgroups of SO(1, 1) Ч E(1, 1).