Consider $g$ a finite-dimensional Lie algebra over the field $k$ and the associative Yang-Baxter equation with spectral parameters:
If A is an associative algebra, we are searching for functions from $\textbf{C}\times \textbf{C}$ to  $A\otimes A$ such that:
$$r^{12}(-u',v)r^{13}(u+u',v+v')-r^{23}(u+u',v')r^{23}(u,v)+r^{13}(u,v+v')r^{23}(u',v')=0$$
For u,u',v,v'
Has the set of the solutions been unravelled ?
In fact, i am searching for solutions which have the unitarity condition, ie :
$$r^{12}(x,y)=-r^{21}(-x,-y)}$$