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Representations of Quantum Groups

  • V. K. Dobrev

Abstract

The q - deformation U q (G) of the universal enveloping algebras U(G) of complex simple Lie algebras G arose in the study of the algebraic aspects of quantum integrable systems [Fa, KR1, KS, Sl, S2, S3]. (The definition of U q (G)is below in Section 1.) They provide a powerful tool for the solving of the quantum Yang-Baxter equations. For recent reviews we refer to [FaT, FRT1,2, J4, Ta, Vg]. The algebras U q (G) are called also quantum groups [Dl, D2] or quantum universal enveloping algebras [Re, KiR1]. In [S3] for(G)= sl(2,c) and in [Drl, J1, J2, Dr2] in general it was observed that the algebras U q (G) have the structure of a Hopf algebra. This brought additional mathematical interest in this new algebraic structure (see, e.g., [R1, Wo, R2, Ve, L1]). Recently, inspired by the Knizhnik-Zamolodchikov equations [KZ] Drinfeld has developed a theory of formal deformations and introduced a new notion of quasi-Hopf algebras [Dr3,4].

Keywords

Hopf Algebra Quantum Group Simple Root Singular Vector Verma Module 
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.

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • V. K. Dobrev
    • 1
  1. 1.Institute of Nuclear Research and Nuclear EnergyBulgarian Academy of SciencesSofiaBulgaria

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