Sliced Extensions, Irreducible Extensions, and Associated Graphs: An Analysis of Lie Algebra Extensions. II. Application to Euclidean, Poincaré, and Galilean Algebras

Abstract

The results of a preceding paper on Lie algebra extensions and sliced extensions are applied to the Lie algebras E(3),P,and G of the Euclidean, resp. Poincaré and Galilean groups. The primitive extensions are analyzed in detail. A procedure for the construction of irreducible extensions is illustrated by some examples, using diagrams which picture the graphs of the extensions. It is proved that all extensions by E(3),P,and G are inessential.