| 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. |
| 关键词: Groebner-Shirshov基 Poincare-Birkhoff-Witt代数 权向量 Gelfand-Kirillov维数 |
| DOI： |
| 分类号:O154.2 |
| 基金项目:Supported by the National Natural Science Foundation of China (11361056). |
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| THE GELFAND-KIRILLOV DIMENSION OF QUANTIZED ENVELOPING ALGEBRA OF TYPE D4 |
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MIAO Yue, ABDUKADIR Obul
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College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
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| Abstract: |
| 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 Gröbner-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. |
| Key words: Grö bner-Shirshov basis Poincaré-Birkhoff-Witt algebra weight vector Gelfand-Kirillov dimension |
