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完备Leibniz代数的性质及其低维分类

PROPERTIES OF COMPLETE LEIBNIZ ALGEBRAS AND THEIR CLASSIFICATION OF LOW DIMENSIONS
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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. 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.
作者 曾阳 林磊
机构地区 华东师范大学数学系
出处 《数学杂志》 CSCD 北大核心 2012年第3期487-498,共12页 Journal of Mathematics
基金 长江学者和创新团队发展计划(PCSIRT) 上海重点学科项目
关键词 LEIBNIZ代数 完备李代数 完备Leibniz代数 Leibniz algebras complete Lie algebras complete Leibniz algebras
分类号 O152.5 [理学—基础数学]
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参考文献11

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数学杂志
2012年 第3期

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