1203.0625 (Adam Bowers)

Three Dimensional Lorentz homogeneous spaces and the Petrov
classification    [PDF]

Adam Bowers

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.

View original: http://arxiv.org/abs/1203.0625