Lie Algebras of Vector Fields in the Real Plane

González‐López, A.; Kamran, Niky; Olver, Peter J.

doi:10.1112/plms/s3-64.2.339

Cited by 127 publications

(244 citation statements)

References 18 publications

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“…The realizations in the real plane presented in Table II are from Mahomed and Leach [43]. These concur with the results of González-Lopéz et al [49] (see also [50]). Table II.…”

Section: Algebrasupporting

confidence: 81%

Symmetry group classification of ordinary differential equations: Survey of some results

Mahomed

2007

Math Methods in App Sciences

112

110

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SUMMARYAfter the initial seminal works of Sophus Lie on ordinary differential equations, several important results on point symmetry group analysis of ordinary differential equations have been obtained. In this review, we present the salient features of point symmetry group classification of scalar ordinary differential equations: linear nth-order, second-order equations as well as related results. The main focus here is the contributions of Peter Leach, in this area, in whose honour this paper is written on the occasion of his 65th birthday celebrations.

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“…The realizations in the real plane presented in Table II are from Mahomed and Leach [43]. These concur with the results of González-Lopéz et al [49] (see also [50]). Table II.…”

Section: Algebrasupporting

confidence: 81%

Symmetry group classification of ordinary differential equations: Survey of some results

Mahomed

2007

Math Methods in App Sciences

112

110

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“…Due to Sophus Lie it is known that the only Lie algebra of first order differential operators which acts on the real line and possesses finite-dimensional representations is the sl(2, R)-algebra (for a discussion see, for example, [21,22]), realized as…”

Section: Introductionmentioning

confidence: 99%

Exact solvability of superintegrable systems

Tempesta

Turbiner

Winternitz

2001

Journal of Mathematical Physics

136

204

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It is shown that all four superintegrable quantum systems on the Euclidean plane possess the same underlying hidden algebra sl(3). The gauge-rotated Hamiltonians, as well as their integrals of motion, once rewritten in appropriate coordinates, preserve a flag of polynomials. This flag corresponds to highest-weight finite-dimensional representations of the sl(3)-algebra, realized by first order differential operators.

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“…In [5], S. Lie has also classified analogous realizations on the complex plane and on the real line. On the real plane such a classification is given in [2].…”

Section: Introductionmentioning

confidence: 99%