# Quaternionic Quantum Groups

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Following the idea of introducing the Hamilton numbers in quantum mechanism, I suggest to define the quaternionic quantum groups. I define the Hopf algebras with the division ring $\bf Q$, the quaternion numbers. So $q \in {\bf Q}$, for example ${\mathfrak sl}_2^{\bf Q}(q)={\bf Q} \otimes_{\bf R} {\mathfrak sl}_2(q)$:

$1\otimes (EF-FE)= \frac{1}{q-q^{-1}}\otimes (K-K^{-1})$