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arXiv · math-ph/0301029

Realizations of Real Low-Dimensional Lie Algebras

Roman O. Popovych·Vyacheslav M. Boyko·Maryna O. Nesterenko·Maxim W. Lutfullin
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Abstract

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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Roman O. Popovych, Vyacheslav M. Boyko, Maryna O. Nesterenko, Maxim W. Lutfullin. 2005-08-04. Realizations of Real Low-Dimensional Lie Algebras. https://doi.org/10.1088/0305-4470%2F36%2F26%2F309

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