# Questions tagged [yang-baxter-equations]

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

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### Permutative Yang-Baxter monoids

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### Quasi-triangular bialgebra construction

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### Yang-Baxter equation for the asymmetric simple exclusion process (ASEP)

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### How can I verify that a given solution of the Quantum Yang-Baxter equation is associated to a given Lie algebra?

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### Solution of the Yang-Baxter equation associated to the $U_q[osp(2n+2|2m)^{(2)}]$ Lie superalgebra

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### Partially permutative matrices

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