Journal of Soviet Mathematics

December 1985, Volume 31, Issue 6, pp 3411–3416 | Cite as

Classical r-matrices and quantization

• Authors
• Authors and affiliations

• M. A. Semenov-Tyan-Shanskii

Article

• 90 Downloads
• 4 Citations

Abstract

The construction of quantum integrals of motion for systems with linear Poisson brackets given by classical r-matrices is described.

Keywords

Poisson Bracket Quantum Integral Linear Poisson Bracket 

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Literature cited

1. 1.
   M. A. Semenov-Tyan-Shanskii, “What is a classical r-matrix,” Funkts. Anal. Prilozhen.,17, No. 4, 17–33 (1983).Google Scholar
2. 2.
   M. A. Semenov-Tyan-Shanskii, “Classical r-matrices and the method of orbits,” in; Differential Geometry, Lie Groups, and Mechanics 5, J. Sov. Math.,28, No. 4 (1985).Google Scholar
3. 3.
   B. Kostant, “Quantization and representation theory” in: Proc. Research Symp. on Representations of Lie Groups, Oxford, 1977, London Math. Soc. Lect. Notes Ser., Vol. 34 (1979), pp. 287–316.Google Scholar
4. 4.
   A. A. Belavin and V. G. Drinfel'd, “Triangle equations and simple Lie algebras,” Preprint ITF-18, Chernogolovka (1982).Google Scholar
5. 5.
   A. G. Reyman and M. A. Semenov-Tyan-Shanskii, “Reduction of Hamiltonian systems, affine Lie algebras, and Lax equations. I,” Invent. Math.,54, 81–100 (1979).CrossRefGoogle Scholar
6. 6.
   M. Duflo, “Operateurs differentiels biinvariants sur un groupe de Lie,” Ann. Sci. Ecole Norm. Sup.,10, 265–283 (1977).Google Scholar
7. 7.
   V. G. Drinfel'd, “Hamiltonian structures on Lie groups, Lie bialgebras, and the geometrical meaning of the Yang-Baxter equation,” Dokl. Akad. Nauk SSSR,268, No. 5, 285–287 (1983).Google Scholar
8. 8.
   N. Yu. Reshetikhin and L. D. Faddeev, “Hamiltonian structures of integrable models of field theory,” Teor. Mat. Fiz.,56, No. 3, 323–343 (1983).Google Scholar
9. 9.
   E. K. Sklyanin, “On some algebraic structures connected with the Yang-Baxter equation. I, II,” Funkts. Anal. Prilozhen.,16, No. 4, 27–34 (1982);17, No. 4, 34–48 (1983).Google Scholar
10. 10.
    V. G. Drinfel'd, “On constant quasiclassical solutions of the Yang-Baxter equation,” Dokl. Akad. Nauk SSSR,273, No. 3, 531–535 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

• M. A. Semenov-Tyan-Shanskii

There are no affiliations available