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Full-Text Articles in Physical Sciences and Mathematics
Decomposing Vector Space Representations Of The Lie Algebras S[2c And S[2r, Brian W. Gleason
Decomposing Vector Space Representations Of The Lie Algebras S[2c And S[2r, Brian W. Gleason
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
It is known that any finite-dimensional representation of a semi-simple Lie algebra is decomposable into a direct sum of irreducible representations. Here we prove some theoretical results that allow us to construct an efficient algorithm for computing such a decomposition for representations of s[2C and s[2R. We then implement this algorithm in a procedure for the computer algebra system Maple that will quickly and easily perform the decomposition. We also give several examples of this decomposition performed by the procedure in order to illustrate its advantages over calculations done ‘by hand'.
The Classification Of Low Dimensional Nilpotent Lie Algebras, Kimberli C. Tripp
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 …