I am going through this paper, 'Quantum entanglement and topological entanglement' by Louis H Kauffman and Samuel J Lomonaco Jr published in New Journal of Physics 4 (2002).
It started with discussing braid operators which I probably get. But on page 6, when it introduces the matrix for a braid operator I don't get the intuition behind it. It is:
\begin{pmatrix} a & 0 &0 &0 \\ 0& 0 &d &0 \\ 0 &c &0 &0 \\ 0 &0 &0 &b \end{pmatrix}
Why is this matrix so? The paper also suggests that it is a solution of the Yang-Baxter equation.