On non-abelian quadrirational Yang–Baxter maps*

Abstract We introduce four non-equivalent lists of families non-abelian quadrirational Yang–Baxter maps, the so-called F , $\mathcal{H}$?> mathvariant="script">H $\mathcal{K}$?> mathvariant="script">K and Λ lists. provide canonical form generic map in each list, which under various degenerations lead to remaining members list. In abelian setting all constitute well known F H maps.