Skip to main content
SpringerLink
Log in

On the Structure of Coboundary R-Matrices of Classical Series

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

Coboundary R-matrices for quantum algebras associated with simple Lie algebras of classical series are computed. In the fundamental representations, these R-matrices are equal to the exponents of the related classical r-matrices. Bibliography: 11 titles.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. L. A. Takhtajan and L. D. Faddeev, Hamiltonian Approach to Solitons Theory[in Russian], Moscow (1986).

  2. N. M. Bogolyubov, A. G. Izergin, and V. E. Korepin, Correlation Functions of Integrable Systems and Quantum Inverse Scattering Method[in Russian], Moscow (1992).

  3. V. G. Drinfeld, "Quantum Groups," in: Proceedings of International Congress of Mathematicians, Vol. 1, Academic Press, New York (1986), pp. 798–820.

    Google Scholar 

  4. L. D. Faddeev, N. Yu. Reshetikhin, and L. A. Takhtajan, Algebra Analiz, 1, 178(1989).

    Google Scholar 

  5. V. Chari and A. Pressley, A Guide to Quantum Groups, Cambridge Univ. Press (1994).

  6. E. E. Demidov, Yu. Manin, E. E. Mukhin, and D. V. Zhadanovich, Prog. Theor. Phys. Suppl., 102, 203(1990).

  7. S. Zakrzewski, Lett. Math. Phys., 22, 287(1991).

    Google Scholar 

  8. J. Hietarinta, "The upper triangular solutions to the three-state constant quantum Yang-Baxter equation," Turku-Fl-P7 (1993).

  9. F. R. Gantmakher, Theory of Matrices[in Russian], Moscow (1988).

  10. S. Zakrzewski, "A characterization of coboundary Poisson Lie groups and Hopf algebras," in: Quantum Groups and Quantum Spaces, Banach Center Publications (1997), pp. 273–278.

  11. M. Gerstenhaber, A. Giaquinto, and S. D. Schak, "Construction of quantum groups from Belavin-Drinfeld infinitesimals," Israel Math. Conf. Proc., 7, 45–64 (1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Military Constructional Engineering, Russia

    E. V. Damaskinskii

  2. St.Petersburg Department of the, Steklov Mathematical Institute, Russia

    P. P. Kulish

  3. St. Petersburg Mechanical Engineering, Russia

    M. A. Sokolov

Authors
  1. E. V. Damaskinskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. P. Kulish
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. A. Sokolov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Damaskinskii, E.V., Kulish, P.P. & Sokolov, M.A. On the Structure of Coboundary R-Matrices of Classical Series. Journal of Mathematical Sciences 115, 1994–2001 (2003). https://doi.org/10.1023/A:1022651813395

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022651813395

Keywords

Search

Navigation