Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups

Abstract

An algorithm for classifying the closed connected subgroups S of a given Lie group G into conjugacy classes, presented in earlier papers, is further refined so as to provide us with ’’normalized’’ lists of representatives of subalgebra classes. The normalized lists contain the subgroup normalizer NorGS (NorGS is the largest subgroup of G for which S is an invariant subgroup) for each subgroup representative. The advantage of having normalized lists is that the problem of merging several different sublists (e.g., the lists of all subgroups of each maximal subgroup of G) into a single overall list becomes greatly simplified. The method is then applied to find all closed connected subgroups of the two de Sitter groups O(3,2) and O(4,1). The classification group in each case is the group of inner automorphisms.