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I tried to understand Belavin-Drinfeld's classification of solutions of classical Yang-Baxter equations. In the book a guide to quantum groups, on page 83, there is an example of solutions of the ...

Let $g= gl_2$. Suppose that $r \in g \otimes g$ satisfies the following properties: (1) $r_{12} + r_{21} \in g \otimes g$ is $g$-invariant, $r_{12} = r$, $r_{21} = \tau \ r_{12}$. (2) $[r_{12}, r_{...