Abstract
The skew-symmetric trigonometric R-matrices in the classification of Belavin and Drinfel'd are shown to be particular elements of a linear set of R-matrices arising from the deformation of the canonical non-skew-symmetric q-pole R-matrix belonging to the Lie algebra G⊗ G⊗ C(λ,μ). This deformation is consistent only on the Lie algebra automorphism defining the q-pole R-matri x is a Coxeter automorphism. This linear deformation is the only one allowed when the algebraic structure of R as an element of G⊗ G is required to be preserved, at least when G=(2, C ).
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