D4型量子包络代数的Gelfand-Kirillov维数
THE GELFAND-KIRILLOV DIMENSION OF QUANTIZED ENVELOPING ALGEBRA OF TYPE D4

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 dimen-sion of quantized enveloping algebra of type D4 by using the method of computing the Gelfand-Kirillov dimension given in [1] and the Gr？bner-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