| 王振,陈惠香.半量子群U≥0[J].数学年刊A辑,2009,30(6):727~740 |
| 半量子群U≥0 |
| The Half-quantum Group U≥0 |
| Received:May 02, 2009 |
| DOI： |
| 中文关键词: 半量子群, 拟余交换, Yetter-Drinfel'd模 |
| 英文关键词:Half-quantum group, Quasi-cocommutative, Yetter-Drinfel'd module |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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