| G2型量子群表示的Grobner—Shirshov基 |
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| 引用本文： | 艾尼·吾司塔,阿布都卡的·吾甫.G2型量子群表示的Grobner—Shirshov基[J].重庆工商大学学报(自然科学版),2013(11):1-5. |
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| 作者姓名： | 艾尼·吾司塔 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,乌鲁木齐830046 |
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| 基金项目： | 国家自然科学基金（11061033）. |
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| 摘 要： | 用单李代数的泛包络代数表示的Grobner-Shirshov基方法，也就是Grobner-Shirshov对（pair）方法，来构造G2型量子群表示的Grobner—Shirshov基是非常苦难的。而用双自由模方法来构造G2型量子群的有限维不可约表示的Grobner—Shirshov基是非常方便的；以已知的G2型量子群的Grobner—Shirshov基为基础．用双自由模方法构造G2型量子群的不可约表示的Grobner-Shirshov基。
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| 关 键 词： | 量子群 Grsbner—Shirshov基 合成 双自由模 最高权模 |
Grobner-Shirshov Basis Represented by G2 -Type Quantum Group |
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| Institution: | Aini Utta, Abdukadir Obul (School of Mathematics and System Science, Xinjiang University, Urumqi 830046, China) |
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| Abstract: | The construction of Grobner-Shirshov Basis represented by G2-type quantum group by Grobner- Shirshov Basis method represented by universal enveloping algebras of simple Lie algebras, i.e. Grobner-Shirshov pair method, is very difficult, however, the construction of Grobner-Shirshov Basis represented by finite dimensional irreducible of G2-type quantum group by double free modules is convenient. By taking Grobner- Shirshov Basis of G2-type quantum group as the basis, this paper uses double free modules method to construct Grobner-Shirshov Basis of irreducible representation of G2-type quantum group. |
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| Keywords: | quantum group Grobner-Shirshov Basis composition double free modules the highest weight module |
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