 RTT construction

Given a Yang-Baxter R-matrix, take generators $t_{ij}$ subject to the displayed matrix relation, with $T_1=T\otimes I$, $T_2=I\otimes T$. The coproduct $\Delta t_{ij}={\sum }_k{t}_{ik}\otimes t_{kj}$ and counit $\epsilon (t_{ij})={\delta }_{ij}$ give a bialgebra. An antipode requires additional inverses or an appropriate determinant quotient; an arbitrary RTT bialgebra is not automatically a Hopf algebra.