D_4型量子包络代数的Gelfand-Kirillov维数（英文）

THE GELFAND-KIRILLOV DIMENSION OF QUANTIZED ENVELOPING ALGEBRA OF TYPE D_4

本文研究了D4型量子包络代数的Gelfand-Kirillov维数的计算问题.利用文献[1]中给出的Gelfand-Kirillov维数的计算方法和文献[2]中给出的D4型量子包络代数的Groebner-Shirshov基计算了D4型量子包络代数的Gelfand-Kirillov维数,得到的主要结果是D4型量子包络代数的Gelfand-Kirillov维数为28.希望此结果为计算Dn型量子包络代数的Gelfand-Kirillov维数提供一些思路.

In this paper,we research the problem of computing the Gelfand-Kirillov dimension of quantized enveloping algebra of type D4 by using the method of computing the GelfandKirillov dimension given in [1] and the Gr¨obner-Shirshov basis for quantized enveloping algebra of type D4 given in [2].The main result we get is that the Gelfand-Kirillov dimension of quantized enveloping algebra of type D4 is 28.We hope this result will provide some ideas to compute the Gelfand-Kirillov dimension of quantized enveloping algebra of type Dn.