Yang–Baxter maps, Darboux transformations, and linear approximations of refactorisation problems
Yang–Baxter maps, Darboux transformations, and linear approximations of refactorisation problems
Yang--Baxter maps (YB maps) are set-theoretical solutions to the quantum Yang--Baxter equation. For a set $X=\Omega\times V$, where $V$ is a vector space and $\Omega$ is regarded as a space of parameters, a linear parametric YB map is a YB map $Y\colon X\times X\to X\times X$ such that $Y$ is …