Abstract
Invertible universal ℛ-matrices of quantum Lie algebras do not exist at roots of unity. However, quotients exist for which intertwiners of tensor products of representations always exist, i.e. ℛ-matrices exist in the representations. One of these quotients, which is finite-dimensional, has a universal ℛ-matrix. In this Letter we answer the following question: under which condition are the different quotients of U q (sl(2)) (Hopf)-equivalent? In the case when they are equivalent, the universal ℛ-matrix of the one can be transformed into a universal ℛ-matrix of the other. We prove that this happens only whenq 4 = 1, and we explicitly give the expressions for the automorphisms and for the transformed universal ℛ-matrices in this case.
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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.
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Arnaudon, D. On automorphisms and universal ℛ-matrices at roots of unity. Lett Math Phys 33, 39–47 (1995). https://doi.org/10.1007/BF00750810
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DOI: https://doi.org/10.1007/BF00750810