The optical group and its subgroups

The optical group Opt(3,1) is a ten-dimensional maximal subgroup of the conformal group of space–time, characterized by the fact that it leaves a lightlike vector subspace in Minkowski space invariant. Thus it is the group underlying the symmetry structure of the parton model in particle physics. The present article is devoted to a complete classification of all closed connected subgroups of Opt(3,1). A list of representatives of all Lie subalgebras of the algebra opt(3,1) is given in the form of tables and many of their properties are established (their invariants, normalizers, isomorphism classes, etc.). Most of the subalgebras of opt(3,1) are also contained in the similitude algebra sim(3,1). We discuss a method for extracting the ’’new’’ subalgebras of opt(3,1) from the list; these will go over into a future list of subalgebras of the conformal Lie algrebra itself.