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Monodromy element: Why that name?

Mathematics Asked on January 26, 2021

Let $(H,R)$ be a quasitriangular Hopf algebra, i.e. $R$ is a choice of an universal $R$-matrix for the Hopf algebra H. (You can find a definition of the term quasitriangular Hopf algebra on wikipedia.).
One calls the element $Q:=R_{21}cdot R_{12} in H otimes H$ the monodromy element of the quasitriangular Hopf algebra $(H,R)$.

Questions

  • Why is $Q$ called that way?
  • Is it related to the monodromy group? Or to any other concept presented on here?

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