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Results tagged with yang-baxter-equations
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user 118681
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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Involutive solutions to the Yang-Baxter equation (and triangular Hopf algebras)
Here is a family of examples indexed by an integer $m\geq 3$.
Let
\begin{eqnarray}
R^{ij}_{kl}=\lambda_{ij}c_{kl}-\delta_{ik}\delta_{jl},\tag{1}
\end{eqnarray}
where $\lambda, c$ are $m\times m$ m …
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