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Results tagged with yang-baxter-equations
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user 521579
In the classical equation, one looks for $R\in\Lambda^2\mathfrak g$ such that $$[R,R]=0,$$ where the bracket is Schouten's bracker in $\Lambda^\bullet\mathfrak g$, the exterior algebra on a Lie algebra $\mathfrak g$. In the quantum one (in its non-parametric form...), one looks for endomorphisms $R:V\otimes V\to V\otimes V$ of tensor squares of vector spaces $V$ such that $$R_{12} \ R_{13} \ R_{23} = R_{23} \ R_{13} \ R_{12},$$
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Accepted
Set-theoretic solutions of YBE for $n=3$
Sure,
degenerate solutions:
\begin{equation}
((1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)),
((1, 1), (1, 2), (3, 1), (2, 1), (2, 2), (3, 2), (1, 3), (2, 3), (3, 3)),
((1, 1) …
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