2012/03/03 by Adam Bowers, Bowers, Adam
Mathematics · Physics and Astronomy · #17B81 #53C30 #53C50 #Advanced Differential Geometry Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Rings and Algebras (math.RA) #math-ph #math.MP #math.RA #msc:17B81 #msc:53C30 #msc:53C50
paper · pdf · doi:10.48550/arxiv.1203.0625
39 pages, 16 tables; adapted from master's thesis
arxiv created 2012/03/03 · openalex publication_date 2012/03/03 · arxiv updated 2012/03/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.