| 泛阶化李超代数 |
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| 引用本文： | 佟洁,张永正.泛阶化李超代数[J].数学学报,2006,49(1):231-240. |
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| 作者姓名： | 佟洁 张永正 |
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| 作者单位： | [1]同济大学理学院应用数学系,上海200092 [2]哈尔滨师范大学数学系,哈尔滨150080 |
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| 基金项目： | 国家自然科学基金资助项目（10271088）教育部高校博士点基金资助项目（20040247024）;致谢 本文第一作者衷心感谢同济大学靳全勤教授给予的悉心指导. |
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| 摘 要： | 对于给定的负阶化李超代数K-,本文定义了K-型泛阶化李超代数并证明了它的存在性．进而引出阶化Cartan型李超代数,并且证得阶化Cartan型李超代数 W(m,n),K(m,n,ωA),S(m,n)和H(m,n)分别可以用某种泛阶化李超代数来刻画．
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| 关 键 词： | 李超代数 泛阶化李超代数 Cartan型李超代数 |
| 文章编号： | 0583-1431（2006）01-0231-10 |
| 收稿时间： | 2005-01-07 |
| 修稿时间： | 2005-01-072005-05-31 |
Universal Graded Lie Superalgebras |
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| Jie TONG, Yong Zhong ZHANG.Universal Graded Lie Superalgebras[J].Acta Mathematica Sinica,2006,49(1):231-240. |
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| Authors: | Jie TONG Yong Zhong ZHANG |
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| Institution: | Jie TONG Department of Applied Mathematics, Tongji University, Shanghai 200092, P. R. China Yong Zhong ZHANG Department of Mathematics, Harbin Normal University, Harbin 150080, P. R. China |
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| Abstract: | For a given negatively graded Lie superalgebra K-, the universal graded Lie superalgrbras U of type K- is defined and its existence is proved. By posing additional conditions on K-, other types of universal graded Lie superalgebras are defined and discussed. The concept of universal graded Lie superalgebras leads naturally to the graded Cartan type Lie superalgebras, and it is proved that the graded Cartan type Lie superalgerbras K(m,n,ωA),S(m,n) and H(m,n) can be characterized as certain universal graded Lie superalgebras. |
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| Keywords: | Lie superalgebra universal graded Lie superalgebra Cartan type Lie superalgebra |
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