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 : $$r^{12}(x,y)=-r^{21}(-x,-y)}$$

Consider $\mathfrak{g}$ a finite-dimensional Lie algebra over the field $\textbf{k}$. 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 $u,u',v,v'\in\mathbb{C}$. This is known as the associative Yang-Baxter equation with spectral parameters. Has the set of the solutions been unravelled when $A=U(\mathfrak{g})$ is the universal envelopping algebra of $\mathfrak{g}$? In fact, I am searching for solutions which have the following unitarity condition: $$r^{12}(x,y)=-r^{21}(-x,-y)$$