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Number of results
Journal
2010 | 8 | 3 | 289-295
Article title

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

Content
Title variants
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.
Publisher

Journal
Year
Volume
8
Issue
3
Pages
289-295
Physical description
Dates
published
1 - 6 - 2010
online
24 - 4 - 2010
Contributors
author
  • Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086, Tallinn, Estonia, eugen.paal@ttu.ee
author
  • Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086, Tallinn, Estonia, jvirkepu@staff.ttu.ee
References
  • [1] O. Babelon, D. Bernard, M. Talon, Introduction to Classical Integrable Systems (Cambridge Univ. Press, 2003)
  • [2] M. Gerstenhaber, Ann. Math. 78, 267 (1963) http://dx.doi.org/10.2307/1970343[Crossref]
  • [3] Ø. Grøn, S. Hervik, Einstein’s General Theory of Relativity (Springer, NewYork, 2007) http://dx.doi.org/10.1007/978-0-387-69200-5[Crossref]
  • [4] L. Landau, E. Lifshitz, Theoretical Physics. Vol. 2: Theory of Field (Moskva, Nauka, 1973) (in Russian)
  • [5] L. Landau, E. Lifshitz, English translation: Course of Theoretical Physics. Vol. 2, The Classical Theory of Fields (Butterworth-Heinemann, Oxford, 1980)
  • [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)
  • [8] E. Paal, J. Virkepu, Rep. Math. Phys. 61, 207 (2008) http://dx.doi.org/10.1016/S0034-4877(08)80008-0[Crossref]
  • [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]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-009-0123-8
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