Three Dimensional Lorentz homogeneous spaces and the Petrov classification
Mathematical Physics
2012-03-06 v1 math.MP
Rings and Algebras
Abstract
In this note, we verify the classification of local geometries given by A.Z. Petrov. First, we determine criteria for identifying a given 3D Lorentz homogeneous space in Petrov's classification. Then, we identify all inequivalent 1D subalgebras of all real 4D Lie algebras and determine which of these give rise to a homogeneous space admitting an invariant Lorentz metric.
Cite
@article{arxiv.1203.0625,
title = {Three Dimensional Lorentz homogeneous spaces and the Petrov classification},
author = {Adam Bowers},
journal= {arXiv preprint arXiv:1203.0625},
year = {2012}
}
Comments
39 pages, 16 tables; adapted from master's thesis