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| 摘要: |
| 令F表示任意域, l2m(F)表示F上Dm型正交李代数的极大幂零子代数.本文的目的是当m ≥ 5时,刻画l2m(F)上的每一个双向保零李括积的映射.利用文献[7]的主要结果和矩阵计算技巧,本文证明了l2m(F)上的一个线性映射φ是双向保零李括积的当且仅当φ能够写成内自同构,图自同构,广义的对角自同构,中心映射,次中心自同构,极端映射和标量乘法的乘积.这推广了文献[7]的主要结果. |
| 关键词: 极大幂零子代数 零李括积 Dm型正交李代数 |
| DOI： |
| 分类号:O151.2 |
| 基金项目:Supported by National Natural Science Foundation of China (11126121); Supported by Doctor Foundation of Henan Polytechnic University (B2010-93); Supported by Natural Science Research Program of Science and Technology Department of Henan Province (112300410120); Supported by Natural Science Research Program of Education Department of Henan Province (2011B110016); Supported by Applied Mathematics Provincial-level Key Discipline of Henan Province. |
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| MAPS PRESERVING ZERO LIE BRACKETS ON A MAXIMAL NILPOTENT SUBALGEBRA OF THE ORTHOGONAL LIE AlGEBRA OF Dm TYPE |
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ZHAO Yan-xiaa,HAN Xue-feng
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| Abstract: |
| Let F be a field, l2m(F) a maximal nilpotent subalgebra of the orthogonal Lie algebra of Dm type. The aim of this paper is to characterize every linear map of l2m(F) which preserves zero Lie brackets in both directions when m ≥ 5. By using the main theorem of the paper [7] and the skill of matrix computation, it is proved that a linear map φ of l2m(F) preserves zero Lie brackets in both directions if and only if φ is the product of an inner automorphism, a graph automorphism, a generalized diagonal automorphism, a central map, a sub-central automorphism, an extremal map and a scalar multiplication. This extends the main result of the paper [7]. |
| Key words: maximal nilpotent subalgebra zero Lie brackets Dm type orthogonal Lie algebra |
