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The Classification Of Low Dimensional Nilpotent Lie Algebras, Kimberli C. Tripp

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Nilpotent Lie algebras are the fundamental building blocks for generic (not semi-simple) Lie algebras. In particular, the classification of nilpotent algebras is the first step in classifying and identifying solvable Lie Algebras. The problem of classifying nilpotent Lie algebras was first studied by Umlauf [9] in 1891. More recently, classifications have been given up to dimension six using different techniques by Morosov (1958) [7], Skjelbred and Sund (1977) [8], and up to dimension five by Dixmier (1958) [2]. Using Morosov's method of classification by maximal abelian ideals, Winternitz reproduced the Morosov classification obtaining different canonical forms for the algebras. The …