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This probably has an easy answer, but is there any sense in which the following statement is true:

Let $U$ be a quantum enveloping algebra with universal $R$-matrix denoted by $R$, then $R$ is unique.

So I am wondering if (1) there is a suitable definition of this uniqueness and (2) where I can find a proof of this statement.

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up vote 1 down vote accepted

R matrices are not unique. See Chari's book for a classification of equivalence.

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thanks! No wonder something like this isn't claimed in Turaev+Kassell. –  Elden Elmanto Jan 26 '13 at 21:30

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