Skip to main content
SpringerLink
Log in

On twisting solutions to the Yang-Baxter equation

  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

Sufficient conditions for an invertible two-tensor F to relate two solutions to the Yang-Baxter equation via the transformation R → F -121 RF are formulated. Those conditions are equivalent to the problem of twisting for certain quasitriangular bialgebras.

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. V.G. Drinfeld: Dokl. Akad. Nauk SSSR 273 (1983) 531.

    Google Scholar 

  2. V.G. Drinfeld: Leningrad Math. J. 1 (1990) 1419.

    Google Scholar 

  3. N.Yu. Reshetikhin: Lett. Math. Pys. 20 (1990) 331.

    Google Scholar 

  4. N.Yu. Reshetikhin and M.A. Semenov-Tian-Shansky: J. Geom. Phys. 5 (1988) 533.

    Google Scholar 

  5. N.Yu. Reshetikhin, L.A. Takhtajan, and L.D. Faddeev: Leningrad Math. J. 1 (1990) 193.

    Google Scholar 

  6. V.G. Drinfeld: in Proc. Int. Congr. Math., Berkeley 1986 (Ed. A.V. Gleason), AMS, Providence, 1987, p. 798.

    Google Scholar 

  7. P.P. Kulish, N.Yu. Reshetikhin, and E.K. Sklyanin: Lett. Math. Phys. 34 (1981) 393.

    Google Scholar 

  8. A. Kempf: in Proc. XXth Conf. on differential geometry methods in theoretical physics, New York 1991 (Eds. S. Catto and A. Rocha), World Scientific, Singapore, 1991, p. 546.

    Google Scholar 

  9. A. Kempf: J. Math. Phys. 35 (1993) 1931.

    Google Scholar 

  10. T. Hodges: Int. Math. Res. Notices 10 (1995) 465.

    Google Scholar 

  11. T. Hodges: Contemp. Math. 214 (1998) 63.

    Google Scholar 

  12. A.D. Jacobs and J.F. Cornwell: Twisting 2-cocycles for the construction of new non-standard quantum groups, q-alg/9702028.

  13. A.I. Mudrov: J. Math. Phys. 39 (1998) 5608.

    Google Scholar 

  14. P.P. Kulish, V.D. Lyakhovsky, and A.I. Mudrov: J. Math. Phys. 40 (1999) 4569.

    Google Scholar 

  15. J. Hietarinta: J. Math. Phys. 34 (1993) 1725.

    Google Scholar 

  16. J.M. Maillet and J. Sanchez de Santos: Drinfel'd twists and algebraic Bethe anzatz, q-alg/9612012.

  17. P.P. Kulish and A. Stolin: Czech. J. Phys. 47 (1997) 1207.

    Google Scholar 

  18. M. Chaichian, P.P. Kulish, and E.V. Damaskinsky: Theor. Math. Phys. 116 (1998) 101.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St.-Petersburg Department, Steklov Mathematical Institute, Fontanka, 27, St.-Petersburg, 191011, Russia

    P.P. Kulish

  2. Department of Theoretical Physics, Institute of Physics, St.-Petersburg State University, Ulyanovskaya, 1, St. Petergof, St.-Petersburg, 198904, Russia

    A.I. Mudrov

Authors
  1. P.P. Kulish
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A.I. Mudrov
    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

Kulish, P., Mudrov, A. On twisting solutions to the Yang-Baxter equation. Czechoslovak Journal of Physics 50, 115–122 (2000). https://doi.org/10.1023/A:1022885317520

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022885317520

Search

Navigation