Realizations of Real Low-Dimensional Lie Algebras

Physics – Mathematical Physics

Scientific paper

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LaTeX2e, 39 pages. Essentially exetended version. Misprints in Appendix are corrected

Scientific paper

10.1088/0305-4470/36/26/309

Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of variables. Our classification amends and essentially generalizes earlier works on the subject. Known results on classification of low-dimensional real Lie algebras, their automorphisms, differentiations, ideals, subalgebras and realizations are reviewed.

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