Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator

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dc.creatorPaal, Eugen
dc.creatorVirkepu, Jyri
dc.date2008-07-02
dc.date2009-05-27
dc.date.accessioned2026-07-07T13:18:01Z
dc.date.available2026-07-07T13:18:01Z
dc.descriptionOperadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.
dc.descriptionLaTeX2e, no figures, 9 pages
dc.identifierhttps://arxiv.org/abs/0807.0428
dc.identifierhttp://arxiv.org/abs/0807.0428
dc.identifierJ. Math. Phys. Vol 50 (2009), 053523, 1-8
dc.identifierdoi:10.1063/1.3131615
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231302
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subject18D50, 70G60
dc.titleDynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator
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