Realizations of real low-dimensional Lie algebras

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Published 18 June 2003 • Published under licence by IOP Publishing Ltd
, , Citation Roman O Popovych et al 2003 J. Phys. A: Math. Gen. 36 7337 DOI 10.1088/0305-4470/36/26/309

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1 Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Str, Kyiv 4, 01601 Ukraine

2 Poltava State Pedagogical University, 2 Ostrogradskoho Str, Poltava, Ukraine

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  1. Received 21 January 2003
  2. Published

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0305-4470/36/26/7337

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.

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