Homogeneous Spaces of the Lorentz Group
Mathematical Physics
2007-05-23 v2 High Energy Physics - Theory
Group Theory
math.MP
Abstract
We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group and all the subalgebras of the Lorentz Lie algebra. We also study the covariant mappings between some pairs of homogeneous spaces. This exercise is done without any claim of originality, but with the hope of providing a useful instrument for the investigation of the Lorentz transformation properties of some physical quantities.
Cite
@article{arxiv.math-ph/0301014,
title = {Homogeneous Spaces of the Lorentz Group},
author = {M. Toller},
journal= {arXiv preprint arXiv:math-ph/0301014},
year = {2007}
}
Comments
25 pages, 1 figure, LATEX file, relevant reference added