| 广义矩阵代数上的非线性Lie中心化子 |
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| 引用本文： | 张芳娟. 广义矩阵代数上的非线性Lie中心化子[J]. 山东大学学报(理学版), 2015, 50(12): 10-14. DOI: 10.6040/j.issn.1671-9352.0.2014.501 |
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| 作者姓名： | 张芳娟 |
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| 作者单位： | 西安邮电大学理学院, 陕西 西安 710121 |
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| 基金项目： | 国家自然科学基金资助项目(11402199);陕西省教育厅科学研究计划自然科学项目(2012JK0873,2012JK0883) |
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| 摘 要： | 令G是广义矩阵代数。若Ф:G→G是非线性Lie中心化子, 在一些微弱的假设下, 得Ф=φ+τ, 其中φ:G→G是可加的中心化子, τ:G→Z(G)对所有x,y∈G, 满足τ[x,y]=0。 作为应用, 获得了因子von Neumann代数、三角代数上非线性Lie中心化子的刻画。
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| 关 键 词： | Lie中心化子 广义矩阵代数 非线性 |
| 收稿时间： | 2014-11-10 |
Nonlinear Lie centralizers of generalized matrix algebras |
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| ZHANG Fang-juan. Nonlinear Lie centralizers of generalized matrix algebras[J]. Journal of Shandong University, 2015, 50(12): 10-14. DOI: 10.6040/j.issn.1671-9352.0.2014.501 |
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| Authors: | ZHANG Fang-juan |
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| Affiliation: | School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, Shaanxi, China |
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| Abstract: | Let G be a generalized matrix algebra. Assume that Ф:G→Gis a nonlinear Lie centralizer. It is shown that, under some mild conditions, Ф can be expressed as Ф=φ+τ, where φ:G→Gis an additive centralizer and τ:G→Z(G) is a mapping that vanishes at commutators. Based on the above results, the characterizations of nonlinear Lie centralizers on factor von Neumann algebras, triangular algebras are obtained. |
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| Keywords: | generalized matrix algebra nonlinear Lie centralizer |
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