Quantum counterparts of three-dimensional real Lie algebras over harmonic oscillator

• Authors: Eugen Paal , Jüri Virkepu
• Languages of publication: EN

Abstracts

EN

Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional (3D) real Lie algebras in Bianchi classification. The Jacobi operators of the quantum algebras are found.

Keywords

EN

Harmonic oscillator; Gerstenhaber brackets; operadic Lax equation; Bianchi classification

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2010
• Volume: 8
• Issue: 3
• Pages: 289-295

Dates

published

1 - 6 - 2010

online

24 - 4 - 2010

Contributors

author

Eugen Paal

• Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086, Tallinn, Estonia

author

Jüri Virkepu

• Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086, Tallinn, Estonia

References

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• [6] P.D. Lax, Commun. Pur. Appl. Math. 21, 467 (1968) http://dx.doi.org/10.1002/cpa.3160210503[Crossref]
• [7] E. Paal, Journal of Generalized Lie Theory and Applications 1, 57 (2007)
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• [9] E. Paal, J. Virkepu, arXiv:0803.0592 [WoS]
• [10] E. Paal, J. Virkepu, Journal of Generalized Lie Theory and Applications 3, 53 (2009) http://dx.doi.org/10.4303/jglta/S090104[Crossref]
• [11] E. Paal, J. Virkepu. J. Math. Phys. 50, 053523 (2009) http://dx.doi.org/10.1063/1.3131615[Crossref]
• [12] E. Paal, J. Virkepu, arXiv:0903.3702. [WoS]

Identifiers

DOI

10.2478/s11534-009-0123-8