| D4型量子包络代数的Gelfand-Kirillov维数 |
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| 引用本文： | 缪玥,阿布都卡的&#;吾甫.D4型量子包络代数的Gelfand-Kirillov维数[J].数学杂志,2015,35(6):1329-1340. |
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| 作者姓名： | 缪玥 阿布都卡的&#;吾甫 |
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| 作者单位： | 新疆大学数学与系统科学学院, 新疆 乌鲁木齐 830046,新疆大学数学与系统科学学院, 新疆 乌鲁木齐 830046 |
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| 基金项目： | Supported by the National Natural Science Foundation of China (11361056). |
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| 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.
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| 关 键 词： | Groebner-Shirshov基 Poincare-Birkhoff-Witt代数 权向量 Gelfand-Kirillov维数 |
| 收稿时间： | 2014/12/15 0:00:00 |
| 修稿时间： | 2015/3/23 0:00:00 |
THE GELFAND-KIRILLOV DIMENSION OF QUANTIZED ENVELOPING ALGEBRA OF TYPE D4 |
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| MIAO Yue and ABDUKADIR Obul.THE GELFAND-KIRILLOV DIMENSION OF QUANTIZED ENVELOPING ALGEBRA OF TYPE D4[J].Journal of Mathematics,2015,35(6):1329-1340. |
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| Authors: | MIAO Yue and ABDUKADIR Obul |
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| Affiliation: | College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China and 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. |
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| Keywords: | Grö bner-Shirshov basis Poincaré-Birkhoff-Witt algebra weight vector Gelfand-Kirillov dimension |
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