Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn (Estonia)
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.
- OSTI ID:
- 21294101
- Journal Information:
- Journal of Mathematical Physics, Vol. 50, Issue 5; Other Information: DOI: 10.1063/1.3131615; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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