Are there some simple way to remember Braid equation and Yang-Baxter equation? The Yang-Baxter equation is $R_{12} R_{13} R_{23} = R_{23} R_{13} R_{12}$ and the Braided equation is $R_{12} R_{23} R_{12} = R_{23} R_{12} R_{23}$. The indices in the equations are complicated. Are there some simple way to remember these indices? Thank you very much.

Take the map $ij \mapsto e_j - e_i$. Then $12$ corresponds to $e_2 - e_1$, $23$ corresponds to $e_3 - e_2$, $13$ corresponds to $e_3 - e_1$. On the left hand side of the Yang-Baxter equation, the simple roots $e_2-e_1$, $e_3 - e_2$ are on the boundary. There sum $e_3 - e_1$ is in the middle. On the right hand side, we also have the simple roots $e_2-e_1$, $e_3 - e_2$ are on the boundary. There sum $e_3 - e_1$ is in the middle.