= RTT construction
{c}
{title2=$RT_1T_2=T_2T_1R$}
= Faddeev-Reshetikhin-Takhtajan construction
{c}
{synonym}
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 $\varepsilon(t_{ij})=\delta_{ij}$ give a <bialgebra>. An antipode requires additional inverses or an appropriate determinant quotient; an arbitrary RTT bialgebra is not automatically a Hopf algebra.
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