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The precise definition of a Quasitriangular Hopf algebra can be found on wikipedia.

What is the reason behind the word "Quasitriangular"?

Is it because the R-matrix is a triangular matrix, or is it related to some properties of triangles?

Thanks for the enlightenment.

Max Demirdilek
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yoyostein
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    Reading this paper (http://people.math.harvard.edu/~yfu/drinfeld_on_almost.pdf) by Drinfeld, might give some insight. He calls the Quantum-Yang-Baxter equation $R_{12}R_{13}R_{23}= R_{23}R_{13}R_{12}$ (which is satisfied by the universal $R$ matrix) the triangular equation. Other sometimes call it the star-triangle equation, I think. I don't know why - maybe others can shine some light on it. – Max Demirdilek Aug 24 '20 at 09:56

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