| 完备Leibniz代数的性质及其低维分类 |
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| 引用本文： | 曾阳,林磊.完备Leibniz代数的性质及其低维分类[J].数学杂志,2012,32(3):487-498. |
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| 作者姓名： | 曾阳 林磊 |
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| 作者单位： | 华东师范大学数学系,上海,200241 |
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| 基金项目： | 长江学者和创新团队发展计划，上海重点学科项目 |
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| 摘 要： | 本文研究了完备Leibniz代数的性质及低维分类.利用Leibniz代数中平方元生成的双边理想,获得了小于五维的完备Leibniz代数完整的分类,以及五维时一类特殊情况下完备Leibniz代数的分类,从而推广了Leibniz代数的结构理论.
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| 关 键 词： | Leibniz代数 完备李代数 完备Leibniz代数 |
PROPERTIES OF COMPLETE LEIBNIZ ALGEBRAS AND THEIR CLASSIFICATION OF LOW DIMENSIONS |
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| ZENG Yang
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LIN Lei.PROPERTIES OF COMPLETE LEIBNIZ ALGEBRAS AND THEIR CLASSIFICATION OF LOW DIMENSIONS[J].Journal of Mathematics,2012,32(3):487-498. |
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| Authors: | ZENG Yang LIN Lei |
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| Institution: | (Dept.of Math.,East China Normal University,Shanghai 200241,China) |
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| Abstract: | In this paper we study the properties of complete Leibniz algebras and their classification of low dimensions.By using the two-sided ideals which are generated by square elements,we obtain complete classification of complete Leibniz algebras of dimension less than five.We also obtain the classification of the special case of five-dimensional complete Leibniz algebras.All these results develop the construction theory of Leibniz algebras. |
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| Keywords: | Leibniz algebras complete Lie algebras complete Leibniz algebras |
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