| 3-李代数的度量结构 |
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| 引用本文： | 白瑞蒲,吴勇,钱丽璞.3-李代数的度量结构[J].河北师范大学学报(自然科学版),2011,35(5). |
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| 作者姓名： | 白瑞蒲 吴勇 钱丽璞 |
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| 作者单位： | 1. 河北大学数学与计算机学院,河北保定,071002
2. 河北体育学院基础部,河北石家庄,050061 |
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| 基金项目： | 国家自然科学基金(10871192); 河北省自然科学基金(A2010000194) |
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| 摘 要： | 研究了特征为2的完备域上5维3-李代数的度量结构,证明了在特征为2的完备域上5维度量3-李代数的导代数维数一定等于4.在导代数维数等于4的5维3-李代数中,任意不变双线性型都是对称不变双线性型,且在F是二元域时,度量维数等于1,在非二元域时度量维数等于2.
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| 关 键 词： | 3-Lie代数 不变双线性型 导代数 度量 |
The Metric Structure of 3-Lie Algebras |
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| BAI Ruipu,WU Yong,QIAN Lipu.The Metric Structure of 3-Lie Algebras[J].Journal of Hebei Normal University,2011,35(5). |
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| Authors: | BAI Ruipu WU Yong QIAN Lipu |
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| Institution: | BAI Ruipu1,WU Yong1,QIAN Lipu2(1.College of Mathematics and Computer Science,Hebei University,Hebei Baoding 071002,China,2.Department of Basic Courses,Hebei Institute of Physical Education,Hebei Shijiazhuang 510061,China) |
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| Abstract: | The structure of 5 dimensional metric 3-Lie algebras is studied.It is proved that the 5 dimensional metric 3-Lie algebras have the 4 diemnsional derived algebra,and every invariant bilinear form is symmetric,furthermore the metric dimension is 1 if F with only two elements,and is 2 in others. |
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| Keywords: | 3-Lie algebra invariant bilinear form derived algebra metric |
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