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Communications in Mathematical Physics

, Volume 149, Issue 2, pp 335–345 | Cite as

Hidden quantum groups inside Kac-Moody algebra

  • A. Alekseev
  • L. Faddeev
  • M. Semenov-Tian-Shansky
Article

Abstract

A lattice analogue of the Kac-Moody algebra is constructed. It is shown that the generators of the quantum algebra with the deformation parameterq=exp(iπ/k+h) can be constructed in terms of generators of the lattice Kac-Moody algebra (LKM) with the central chargek. It appears that there exists a natural correspondence between representations of the LKM algebra and the finite dimensional quantum group. The tensor product for representations of the LKM algebra and the finite dimensional quantum algebra is suggested.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Tensor Product 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • A. Alekseev
    • 1
  • L. Faddeev
    • 1
  • M. Semenov-Tian-Shansky
    • 1
  1. 1.St. Petersburg Branch of Steklov Mathematical InstituteSt. PetersburgRussia

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