| 路李代数及其性质 |
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| 引用本文： | 高凤霞,韩红梅. 路李代数及其性质[J]. 曲阜师范大学学报, 2007, 33(4): 29-32 |
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| 作者姓名： | 高凤霞 韩红梅 |
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| 作者单位： | 曲阜师范大学数学科学学院;曲阜师范大学《中学数学杂志》编辑部,273165,山东省曲阜市 |
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| 摘 要： | 对路李代数及其性质做了研究.给出了有限维路李代数均可解的结论和所有的卡当子代数；并给出了其相对于一个特定的卡当子代数的根子空间的分解；最后，对一类无限维路李代数可解的条件作了探讨.
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| 关 键 词： | 路李代数 可解李代数 幂零李代数 卡当子代数 |
| 文章编号： | 1001-5337（2007）04-0029-04 |
| 修稿时间： | 2006-12-28 |
Path Lie Algebras and Their Properties |
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| GAO Feng-xia,HAN Hong-mei. Path Lie Algebras and Their Properties[J]. Journal of Qufu Normal University(Natural Science), 2007, 33(4): 29-32 |
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| Authors: | GAO Feng-xia HAN Hong-mei |
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| Affiliation: | 1. School of Mathematical Science; 2. Department of Magzine of Middle School Mathematics, Qufu Normal University, 273165, Qufu, Shandong, PRC |
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| Abstract: | In this paper, the path Lie algebras and their properties are studied. All finite-dimensional path lie algebras are solvable and their Cartan subalgebras of them are obtained. The root space decompositions of them relative to specific Cartan subalgebras are given. Finally, the solvability of a kind of infinitedimensional path Lie algebras is disscussed. |
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| Keywords: | path Lie algebras solvable Lie algebras nilpotent Lie algebras Cartan subalgebras |
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