Communications in Mathematical Physics

, Volume 141, Issue 3, pp 599–617

UniversalR-matrix for quantized (super)algebras

  • S. M. Khoroshkin
  • V. N. Tolstoy

DOI: 10.1007/BF02102819

Cite this article as:
Khoroshkin, S.M. & Tolstoy, V.N. Commun.Math. Phys. (1991) 141: 599. doi:10.1007/BF02102819


For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A. N. Kirillov, and N. Reshetikhin, Ya. S. Soibelman, and S. Z. Levendorskii. Our approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties ofq-exponential functions. We don't use quantum Weyl group.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • S. M. Khoroshkin
    • 1
  • V. N. Tolstoy
    • 2
  1. 1.Institute of New TechnologiesMoscowUSSR
  2. 2.Institute of Nuclear PhysicsMoscow State UniversityMoscowUSSR