| 交换环上严格上三角矩阵的广义李三导子(英文) |
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| 引用本文： | 李海玲,王颖.交换环上严格上三角矩阵的广义李三导子(英文)[J].数学杂志,2012,32(2):253-262. |
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| 作者姓名： | 李海玲 王颖 |
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| 作者单位： | 1. 山东理工大学理学院,山东淄博,255049
2. 大连理工大学数学科学学院,辽宁大连,116024 |
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| 基金项目： | Supported by National Natural Science Foundation of China(10771027) |
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| 摘 要： | 本文研究了交换环R上所有n×n严格上三角矩阵构成的李代数N(n,R)(n≥5)上广义李三导子.利用矩阵技巧,证明了N(n,R)(n≥5)上任意广义李三导子为一李三导子与一位似映射的和.对于N(n,R)(n≥3)上广义李导子,得出类似结果.
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| 关 键 词： | 广义李三导子 广义李导子 严格上三角矩阵 位似 |
GENERALIZED LIE TRIPLE DERIVATIONS OF STRICTLY UPPER TRIANGULAR MATRICES OVER A COMMUTATIVE RING |
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| LI Hai-ling
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WANG Ying.GENERALIZED LIE TRIPLE DERIVATIONS OF STRICTLY UPPER TRIANGULAR MATRICES OVER A COMMUTATIVE RING[J].Journal of Mathematics,2012,32(2):253-262. |
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| Authors: | LI Hai-ling WANG Ying |
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| Institution: | 1.School of Science,Shandong University of Technology,Zibo 255049,China)(2.School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China) |
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| Abstract: | In this article,we mainly study generalized Lie triple derivations for the Lie algebra N(n,R)(n ≥ 5) consisting of all n×n strictly upper triangular matrices over a commutative ring R.Using matrix technique,we prove that every generalized Lie triple derivation of N(n,R)(n ≥ 5) is the sum of a Lie triple derivation and a homothety.A similar result for generalized Lie derivations of N(n,R)(n ≥ 3) is also obtained. |
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| Keywords: | generalized Lie triple derivation generalized Lie derivation strictly upper triangular matrix homothety |
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