| 关于Hom-李代数的结构 |
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| 引用本文： | 王圣祥,张晓辉.关于Hom-李代数的结构[J].数学研究及应用,2014,34(4):459-466. |
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| 作者姓名： | 王圣祥 张晓辉 |
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| 作者单位： | 滁州学院数学科学学院, 安徽 滁州 239000;东南大学数学系, 江苏 南京 210096 |
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| 基金项目： | 安徽省优秀人才青年基金项目(Grant No.2013SQRL092ZD);安徽省自然科学基金项目(Grant Nos.1408085QA06;1408085QA08);滁州学院优秀人才青年基金项目(Grant No.2013RC001);江苏省研究生培养创新工程项目(Grant No.CXLX12-0071). |
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| 摘 要： | Let A be a multiplicative Hom-associative algebra and L a multiplicative Hom-Lie algebra together with surjective twisting maps. We show that if A is a sum of two commutative Hom-associative subalgebras, then the commutator Hom-ideal is nilpotent. Furthermore, we obtain an analogous result for Hom-Lie algebra L extending Kegel＇s Theorem. Finally, we discuss the Hom-Lie ideal structure of a simple Hom-associative algebra A by showing that any non-commutative Hom-Lie ideal of A must contain A, A].
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| 关 键 词： | 李代数 结构 结合代数 代数和 理想 非交换 乘法 扭曲 |
| 收稿时间： | 2012/12/1 0:00:00 |
| 修稿时间： | 2014/4/16 0:00:00 |
On the Structures of Hom-Lie Algebras |
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| Shengxiang WANG and Xiaohui ZHANG.On the Structures of Hom-Lie Algebras[J].Journal of Mathematical Research with Applications,2014,34(4):459-466. |
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| Authors: | Shengxiang WANG and Xiaohui ZHANG |
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| Institution: | School of Mathematics Sciences, Chuzhou University, Anhui 239000, P. R. China;Department of Mathematics, Southeast University, Jiangsu 210096, P. R. China |
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| Abstract: | Let $A$ be a multiplicative Hom-associative algebra and $L$ a multiplicative Hom-Lie algebra together with surjective twisting maps. We show that if $A$ is a sum of two commutative Hom-associative subalgebras, then the commutator Hom-ideal is nilpotent. Furthermore, we obtain an analogous result for Hom-Lie algebra $L$ extending Kegel's Theorem. Finally, we discuss the Hom-Lie ideal structure of a simple Hom-associative algebra $A$ by showing that any non-commutative Hom-Lie ideal of $A$ must contain $A,A].$ |
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| Keywords: | Hom-associative algebra Hom-Lie algebra Kegel's theorem |
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