Why is the R-matrix of a Hopf algebra called unitary when it satisfies the relation $$R^{-1}=R_{12},$$ I would say invertible, why then call it unitary? Is that a nomenclature that maybe comes from physics?
2026-03-26 07:58:41.1774511921
A triangular Hopf algebra and its unitary R-matrix
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If $R^{-1}=R_{12}$, then the square of the braiding is equal to one, i.e. the category of $H$-modules is symmetric monoidal. I don't think "unitary" is good terminology and am not sure if it is standard, but "invertible" would not be good terminology because that simply means that $R^{-1}$ exists.