| 半量子群u~(≥0) |
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| 引用本文： | 王振,陈惠香.半量子群u~(≥0)[J].数学年刊A辑,2009,30(6). |
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| 作者姓名： | 王振 陈惠香 |
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| 作者单位： | 1. 盐城工学院基础部,江苏,盐城,224003
2. 扬州大学数学科学学院,江苏,扬州,225002 |
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| 基金项目： | 国家自然科学基金，教育部博士点基金(No.200811170001)资助的项目 |
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| 摘 要： | 设u~(≥0)表示一个固定单李代数的半量子群,给出了u~(≥0)的性质和表示.证明了Hopf代数u~(≥0)不是拟余交换的,因此左u~(≥0)-模范畴不是辫子monoidal范畴.在权模范畴W中,给出了所有单对象和投射对象.最后描述了所有单的Yetter-Drinfel'd u~(≥0)-权模.
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| 关 键 词： | 半量子群 拟余交换 Yetter-Drinfel'd模 |
The Half-quantum Group u~(≥0) |
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| WANG Zhen,CHEN Huixiang.The Half-quantum Group u~(≥0)[J].Chinese Annals of Mathematics,Series A,2009,30(6). |
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| Authors: | WANG Zhen CHEN Huixiang |
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| Abstract: | Let u~(≥0) denote the half-quantum group for a fixed simple Lie algebra. This paper examines some properties and representation of u~(≥0). The authors prove that the Hopf algebra u~(≥0) is not quasi-cocommutative, and hence the category of left u~(≥0) -module is not a braided monoidal category. In the weight module category W, all the simple objects and the projective objects are described. And all simple Yetter-Drinfel'd u~(≥0)-weight modules are also described. |
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| Keywords: | Half-quantum group Quasi-cocommutative Yetter-Drinfel'd module |
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