Physics – Mathematical Physics
Scientific paper
2003-01-21
J.Phys. A36 (2003) 7337-7360
Physics
Mathematical Physics
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.
Boyko Vyacheslav M.
Lutfullin Maxim W.
Nesterenko Maryna O.
Popovych Roman O.
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