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Realizations of real low-dimensional Lie algebras

Roman O Popovych et al 2003 J. Phys. A: Math. Gen. 36 7337-7360   doi: 10.1088/0305-4470/36/26/309  Help

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Roman O Popovych1, Vyacheslav M Boyko1, Maryna O Nesterenko1 and Maxim W Lutfullin2
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
E-mail: rop@imath.kiev.ua, boyko@imath.kiev.ua and nmo@imath.kiev.ua and MWL@beep.ru

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.

PACS numbers: 02.20.Sv, 02.30.Jr, 02.40.Vh

Print publication: Issue 26 (4 July 2003)
Received 21 January 2003
Published 18 June 2003

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