| B_3-型量子群的 Gelfand-Kirillov 维数 |
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| 引用本文： | 阿依古力·热西提,阿布都卡的·吾甫.B_3-型量子群的 Gelfand-Kirillov 维数[J].四川大学学报(自然科学版),2017,54(2):253-260. |
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| 作者姓名： | 阿依古力·热西提 阿布都卡的·吾甫 |
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| 作者单位： | 新疆大学, |
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| 摘 要： | 本文旨在计算B_3-型量子群的Gelfand-Kirillov维数,所用方法是:首先利用RingelHall代数方法计算B_3-型量子群的所有根向量之间的拟交换公式,然后利用相应的B_3-型量子群的Grobner-Shirshov基计算B_3-型量子群的Gelfand-Kirillov维数,得到的主要结果是B_3-型量子群的Gelfand-Kirillov维数等于21.
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| 关 键 词： | Gr\"{o}bner-Shirshov 基 Poincare-Birkhoff-Witt 代数 权向量 Gelfand-Kirillov 维数 |
| 收稿时间： | 2016/9/16 0:00:00 |
| 修稿时间： | 2016/11/1 0:00:00 |
Gelfand-Krillov dimension of quantum group of type B_3 |
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| Aygul Rexit and Abdukadir Obul.Gelfand-Krillov dimension of quantum group of type B_3[J].Journal of Sichuan University (Natural Science Edition),2017,54(2):253-260. |
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| Authors: | Aygul Rexit and Abdukadir Obul |
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| Institution: | College of Mathematics and System Sciences, Xinjiang University and College of Mathematics and System Sciences, Xinjiang University |
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| Abstract: | The aim of this paper is to compute the Gelfand-Krillov dimension of quantum group of type $B_3$. The method is, first, compute all skew-commutator relations between
all root vectors of quantum group of type $B_3$ by using Ringel-Hall algebra approach, then using the corresponding Gr\"{o}bner-Shirshov basis compute the Gelfand-Krillov dimension of quantum group of type $B_3$. The main result is that the Gelfand-Krillov dimension of quantum group of type $B_3$ is 21. |
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| Keywords: | Gr\"{o}bner-Shirshov basis Poincare-Birkhoff-Witt algebra weight vectors Gelfand-Kirillov dimension |
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