The oscillator group as a homogeneous spacetime

Abstract

Some results on the oscillator group are reported. Specifically: some of their properties as a causal homogeneous spacetime; the oscillator group as a symmetric Lorentzian space which is solution of sourceless Einstein-Yang-Mills equations; the Lorentzian homogeneous structures and their associated groups of isometries on the oscillator group with left-invariant Lorentzian metrics; the Lorentzian homogeneous structures associated to a bi-invariant metric; and then the oscillator group as solution of Einstein-Yang-Mills equations with sources.Partially supported by DGES (Spain) under Project PB95-0124 and by Xuna de Galicia under Project SUGA 20703B98Peer Reviewe