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arXiv · 0807.0428

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

Eugen Paal·Jyri Virkepu
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Abstract

Operadic 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.

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BibTeXRIS

Eugen Paal, Jyri Virkepu. 2009-05-27. Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator. https://doi.org/10.1063/1.3131615

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