Gelfand-Krillov dimension of quantum group of type B_3

Abstract:

The aim of this paper is to compute the Gelfand-Krillov dimension of quantum group of type $B_3$. The method is, first, compute all skew-commutator relations between all root vectors of quantum group of type $B_3$ by using Ringel-Hall algebra approach, then using the corresponding Gr\"{o}bner-Shirshov basis compute the Gelfand-Krillov dimension of quantum group of type $B_3$. The main result is that the Gelfand-Krillov dimension of quantum group of type $B_3$ is 21.