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

作　　者：缪玥 阿布都卡的.吾甫 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学杂志》2015年第6期1329-1340,共12页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(11361056)

摘　　要：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.

关 键 词：Groebner-Shirshov基 Poincare-Birkhoff-Witt代数 权向量 Gelfand-Kirillov维数 

分 类 号：O154.2[理学—数学]