= Quantum enveloping algebra of sl2
{title2=$U_q(\mathfrak{sl}_2)$}
Over a <field> with $q\ne0$ and $q^2\ne1$, this <Hopf algebra> has generators $E,F,K,K^{-1}$ and relations $KE=q^2EK$, $KF=q^{-2}FK$ and $EF-FE=(K-K^{-1})/(q-q^{-1})$. One <comultiplication> convention is $\Delta E=E\otimes K+1\otimes E$, $\Delta F=F\otimes1+K^{-1}\otimes F$ and $\Delta K=K\otimes K$. Its <counit> takes $E,F$ to zero and $K$ to one. The <antipode> takes $E$ to $-EK^{-1}$, $F$ to $-KF$ and $K$ to $K^{-1}$.
Back to article page
