| n-李代数的交换子代数与交换理想 |
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| 引用本文： | 白瑞蒲,张丽红,吴勇. n-李代数的交换子代数与交换理想[J]. 黑龙江大学自然科学学报, 2012, 0(4): 421-425 |
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| 作者姓名： | 白瑞蒲 张丽红 吴勇 |
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| 作者单位： | 河北大学数学与计算机学院 |
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| 基金项目： | 国家自然科学基金资助项目(10871192);河北省自然科学基金资助项目(A2010000194) |
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| 摘 要： | 讨论n-李代数的结构。研究n-李代数的交换子代数的最大维数α(L)与交换理想的最大维数β(L)的性质,证明特征为零的代数闭域上有限维n-李代数L的交换理想的最大维数为dimL-n+1。详细讨论所有维数小于等于n+2的n-李代数的α(L)与β(L)。
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| 关 键 词： | n-李代数 交换子代数 交换理想 |
Abelian subalgebras and Abelian ideals of n-Lie algebras |
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| BAI Rui-pu,ZHANG Li-hong,WU Yong. Abelian subalgebras and Abelian ideals of n-Lie algebras[J]. Journal of Natural Science of Heilongjiang University, 2012, 0(4): 421-425 |
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| Authors: | BAI Rui-pu ZHANG Li-hong WU Yong |
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| Affiliation: | (College of Mathematics and Computer Science,Hebei University,Baoding 071002,China) |
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| Abstract: | The structures of n-Lie algebras is investigated.The properties of the maximal dimension α(L) of abelian subalgebras and the maximal dimension β(L) of abelian ideals are studied.It is proven that for every finite-dimensional n-Lie algebra L over an algebraically closed field of characteristic zero,β(L)≤dimL-n+1.And α(L) and β(L) of n-Lie algebras L with dimL≤n+2 are discussed. |
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| Keywords: | n-Lie algebra Abelian subalgebra Abelian ideal |
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