Realizations of Real Low-Dimensional Lie Algebras

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.

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

References in corpus (5)

• Group classification of heat conductivity equations with a nonlinear source
• Automorphisms of Real 4 Dimensional Lie Algebras and the Invariant Characterization of Homogeneous 4-Spaces
• Solvable Lie algebras with triangular nilradicals
• Invariants of the nilpotent and solvable triangular Lie algebras
• Four dimensional Lie symmetry algebras and fourth order ordinary differential equations

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• Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements
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• Invariant Poisson-Nijenhuis structures on Lie groups and classification
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• Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds
• Jacobi-Lie Hamiltonian systems on real low-dimensional Jacobi-Lie groups and their Lie symmetries
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