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

Abstract

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