Poltava State Pedagogical University,
2 Ostrogradskoho Str., Poltava, UKRAINE
Realizations of low-dimensional Lie algebras
Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of 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. Some applications of obtained results are also discussed.
The talk is based on our work math-ph/0301029 (J. Phys. A, 2003, V.36, 7337-7360).