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Communications in Mathematical Physics

, Volume 161, Issue 1, pp 125–156 | Cite as

The hidden group structure of quantum groups: Strong duality, rigidity and preferred deformations

  • P. Bonneau
  • M. Flato
  • M. Gerstenhaber
  • G. Pinczon
Article

Abstract

A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients andC-functions. Strong rigidity (H bi 2 ={0}) under deformations in the category of bialgebras is proved and consequences are deduced.

Keywords

Neural Network Statistical Physic Complex System Generic Model Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • P. Bonneau
    • 1
  • M. Flato
    • 1
  • M. Gerstenhaber
    • 2
  • G. Pinczon
    • 1
  1. 1.Laboratoire de Physique MathématiqueUniversité de BourgogneDijon CedexFrance
  2. 2.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

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