中文摘要：

本文旨在计算B3-型量子群的Gelfand—Kirillov维数，所用方法是：首先利用Ringel—Hall代数方法计算B3-型量子群的所有根向量之间的拟交换公式，然后利用相应的B-型量子群的Grobner—Shirshov基计算B3-型量子群的Gelfand—Kirillov维数，得到的主要结果是B3-型量子群的Oelfand—Kirillov维数等于21．

英文摘要：

The aim of this paper is to compute the Gelfand-Kirillov dimension of quantum group of type B3. Firstly, we compute all skew-commutator relations between all root vectors of quantum group of type B3by using the Ringel-Hall algebra approach. Then,by using the corresponding Groebner-Shirshov basis, we compute the Gelfand-Kirillov dimension of quantum group of type B3. The main result is that the Gelfand-Kiriliov dimension of quantum group of type B3 is 21.