Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups

TL;DR

This paper provides a geometric proof for the classification of certain subalgebras of Lorentzian Lie algebras and classifies isometry and similarity groups acting transitively on Lobachevskian and Euclidean spaces.

Contribution

It offers a geometric proof for the classification of weakly-irreducible subalgebras of a9(1,n+1) and classifies transitive isometry and similarity groups.

Findings

Classification of weakly-irreducible subalgebras of a9(1,n+1)

Geometric proof approach for algebra classification

Complete classification of transitive isometry and similarity groups

Abstract

Weakly-irreducible not irreducible subalgebras of $\so(1,n+1)$ were classified by L. Berard Bergery and A. Ikemakhen. In the present paper a geometrical proof of this result is given. Transitively acting isometry groups of Lobachevskian spaces and transitively acting similarity transformation groups of Euclidean spaces are classified.