Yang-Baxter and the Boost: splitting the difference

In this paper we continue our classification of regular solutions the Yang-Baxter equation using method based on spin chain boost operator developed in \cite{deLeeuw:2019zsi}. We provide details how to find all non-difference form and apply chains with local Hilbert space dimensions two, three four. classify $16\times 16$ which exhibit $\mathfrak{su}(2)\oplus \mathfrak{su}(2)$ symmetry, include one-dimensional Hubbard model $S$-matrix ${\rm AdS}_5 \times {\rm S}^5$ superstring sigma model. cases interesting novel equation.