Roman POPOVYCH, Vyacheslav BOYKO, Maryna NESTERENKO
Department of Applied Research,
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv-4, UKRAINE
E-mail: rop@imath.kiev.ua, boyko@imath.kiev.ua, nmo@imath.kiev.ua

Maxim LUTFULLIN
Poltava State Pedagogical University,
2 Ostrogradskoho Str., Poltava, UKRAINE
E-mail: MWL@pdpu.septor.net.ua

Realizations of 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 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).