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Let $G_q$ be the $q$-deformation of a simply connected simple compact Liegroup $G$ of type $A$, $C$ or $D$ and $\mathcal{O}_q(G)$ be the algebra ofregular functions on $G_q$. In this article, we prove that the Gelfand-Kirillovdimension of $\mathcal{O}_q(G)$ is equal to the dimension of real manifold $G$.

Gelfand-Kirillov dimension of the algebra of regular functions on quantum groups