[1]费秀海,戴 磊,张海芳.三角代数上的非线性(m,n)-Lie中心化子[J].南京师范大学学报(自然科学版),2019,42(01):23.[doi:10.3969/j.issn.1001-4616.2019.01.005]
　Fei Xiuhai,Dai Lei,Zhang Haifang.Nonlinear(m,n)-Lie Centralizers on Triangular Algebras[J].Journal of Nanjing Normal University(Natural Science Edition),2019,42(01):23.[doi:10.3969/j.issn.1001-4616.2019.01.005]
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三角代数上的非线性(m,n)-Lie中心化子()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第42卷
期数:
2019年01期
页码:
23
栏目:
·数学·
出版日期:
2019-03-20

文章信息/Info

Title:
Nonlinear(m,n)-Lie Centralizers on Triangular Algebras
文章编号:
1001-4616(2019)01-0023-05
作者:
费秀海1; 戴 磊2; 张海芳1
(1.滇西科技师范学院数学系,云南 临沧 677000)(2.渭南师范学院数学与信息科学学院,陕西 渭南 714099)
Author(s):
Fei Xiuhai1; Dai Lei2; Zhang Haifang1
(1.Department of Mathematics,Dianxi Science and Technology Normal University,Lincang 677099,China)(2.College of Mathematics and Information Science,Weinan Normal University,Weinan 714099,China)
关键词:
三角代数; 中心化子; Lie中心化子; 非线性(m; n)-Lie中心化子
Keywords:
triangular algebra; centralizer; Lie centralizer; nonlinear(m; n)-Lie centralizer
分类号:
O177.1
DOI:
10.3969/j.issn.1001-4616.2019.01.005
文献标志码:
A
摘要:
设m,n是固定的整数且(m+n)(m-n)≠0,U是一个|(m+n)(m-n)|-无挠的三角代数且满足πA(Z(U))=Z(A)和πB(Z(U))=Z(B). 若L是U上的一个非线性(m,n)-Lie中心化子,则存在一个中心元λ和一个到U的中心且在交换子上为零的映射ξ使得对任意的x∈U,有L(x)=λx+ξ(x).
Abstract:
Let m,n be fixed integers with(m+n)(m-n)≠0,U be a |(m+n)(m-n)|-torsion free triangular algebra with πA(Z(U))=Z(A)and πB(Z(U))=Z(B). If L is a nonlinear(m,n)-Lie centralizer from Uinto itself,then there exist a center element λ and a mapping ξ from Uinto Z(U)vanishing on all commutators such that L(x)=λx+ξ(x)for all x∈U.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2018-03-16.
基金项目:国家自然科学基金项目(11471199)、陕西省自然科学基础研究计划资助项目(2014JQ1015).
通讯联系人:费秀海,博士,副教授,研究方向:算子代数与算子理论. E-mail:xiuhaifei@snnu.edu.cn
更新日期/Last Update: 2019-03-30