Contractions of the Low-Dimensional Real Lie Algebras

Abstract

A complete and detailed classification and analysis of all the Inonu-Wigner contractions of all the real Lie algebras of dimension 1, 2, and 3 is presented. Starting with a more natural classification of the algebras, many corrections and completions are made to the earlier results of Sharp. Among other things, a proper contraction is constructed between two three-dimensional Lie algebras both of which have two-dimensional derived algebras-a phenomenon previously claimed impossible.