Popovych, Roman O.; Boyko, Vyacheslav M.; Nesterenko, Maryna O.; Lutfullin, Maxim W. Realizations of real low-dimensional Lie algebras. (English) Zbl 1040.17021 J. Phys. A, Math. Gen. 36, No. 26, 7337-7360 (2003). Summary: 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. Cited in 75 Documents MSC: 17B66 Lie algebras of vector fields and related (super) algebras 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain PDFBibTeX XMLCite \textit{R. O. Popovych} et al., J. Phys. A, Math. Gen. 36, No. 26, 7337--7360 (2003; Zbl 1040.17021) Full Text: DOI arXiv