Subspaces of Real Four-Dimensional Lie Algebras: a Classification of Subalgebras, Ideals, and Full-Rank Subspaces

Subspaces of Real Four-Dimensional Lie Algebras: a Classification of Subalgebras, Ideals, and Full-Rank Subspaces

We classify the subspaces of each real four-dimensional Lie algebra, up to automorphism. Enumerations of the subalgebras, ideals, and full-rank (or bracket generating) subspaces are obtained. Also, the interplay between quotients (resp. extensions) of algebras and such classifications is briefly con...

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Veröffentlicht in:Extracta mathematicae 2015, Vol.30 (1), p.41-93
Hauptverfasser: Remsing, Claudiu C, Biggs, Rory
Format: Artikel
Sprache:eng
Schlagworte:
ideal
Lie algebra
subalgebra
subspace
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Zusammenfassung:We classify the subspaces of each real four-dimensional Lie algebra, up to automorphism. Enumerations of the subalgebras, ideals, and full-rank (or bracket generating) subspaces are obtained. Also, the interplay between quotients (resp. extensions) of algebras and such classifications is briefly considered.
ISSN:0213-8743
2605-5686