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On universal R-matrices at roots of unity

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Czechoslovak Journal of Physics Aims and scope

Abstract

It is well-known that quantum algebras at roots of unity are not quasi-triangular. They indeed do not possess an invertible universalR-matrix. They have, however, families of quotients, on which no obstructiona priori forbids the existence an universalR-matrix. In particular, the universalR-matrix of the so-called finite dimensional quotient is already known. We try here to answer the following questions: are most of these quotients equivalent (or Hopf equivalent)? Can the universalR-matrix of one be transformed to the universalR-matrix of another using isomorphisms?

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Authors and Affiliations

  1. Laboratoire de Physique Théorique ENSLAPP, Chemin de Bellevue BP 110, 74941, Annecy-le-Vieux Cedex, France

    Daniel Arnaudon

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  1. Daniel Arnaudon
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URA 14-36 du CNRS, associée à l'E.N.S. de Lyon et au L.A.P.P. d'Annecy-le-Vieux.

I thank the organisers of this colloquium for the nice atmosphere they create each year at Prague. Michel Bauer and Frank Thuillier are warmfully thanked for discussions and fruitful remarks. The author also thanks N. Reshetikhin for an interesting discussion on automorphisms ofU q (sl(2)).

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Arnaudon, D. On universal R-matrices at roots of unity. Czech J Phys 44, 973–980 (1994). https://doi.org/10.1007/BF01690449

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  • DOI: https://doi.org/10.1007/BF01690449

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