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Results tagged with yang-baxter-equations
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user 17845
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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Examples of Yang-Baxter monoids
What about using the theory of braces? A skew brace is a triple $(A,+,\circ)$, where $(A,+)$ and $(A,\circ)$ are groups and $a\circ (b+c)=a\circ b-a+a\circ c$ holds for all $a,b,c\in A$. Notation: If …
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