算子代数上的Lie可导映射

数学物理学报 ›› 2014, Vol. 34 ›› Issue (1): 39-48.

算子代数上的Lie可导映射

安润玲, Kichi-Suke Saito

太原理工大学数学系太原 030024|Department of Mathematics, Niigata University, |Niigata 950-2181, Japan

收稿日期:2011-03-08 修回日期:2013-04-18 出版日期:2014-02-25 发布日期:2014-02-25
基金资助:
国家自然科学基金(11001194)和山西省自然科学基金(2009021002)资助.

Lie Derivable Maps on Operator Algebras

AN Run-Ling, Kichi-Suke Saito

School of Mathematics, Taiyuan University of Technology, Taiyuan 030024|Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan

Received:2011-03-08 Revised:2013-04-18 Online:2014-02-25 Published:2014-02-25
Supported by:
国家自然科学基金(11001194)和山西省自然科学基金(2009021002)资助.

摘要/Abstract

摘要：

设A为有单位且包含一非平凡幂等元的环, M为A双模. 称δ: A→M为Lie可导映射(无可加或连续假设), 若δ([A, B])=[δ(A), B]+[A, δ(B)], ∨A, B∈A. 在一定条件下该文证明了Lie可导映射δ具有形式δ(A)=τ(A)+f(A), 其中τ: A→M是可加导子, f是从A到M的中心且满足f([A, B])=0 , ∨A, B∈A的映射. 由此刻画了因子von Neuamnn代数和套代数上的Lie可导映射.

关键词: Lie可导映射, 因子von Neuamnn代数, 套代数

Abstract:

Let A be a unital algebra, and let M be an A-bimodule. We say δ: A→M is a Lie derivable map if it (with no assumption of additivity and continuity) satisfies δ([A, B])=[δ(A), B]+[A, δ(B)] for all A, B∈A. Under some condition, we show that δ is of the form δ(A)=τ(A)+f(A), where τ: A→M is an additive derivation and f is a map from A into the center of M with f([A, B])=0 for all A, B∈A. As its application, we characterize Lie derivable maps on factor von Neumann algebras and nest algebras.

Key words: Lie derivable maps, Factor von Neumann algebras, Nest algebras

中图分类号:

16W25

安润玲, Kichi-Suke Saito. 算子代数上的Lie可导映射[J]. 数学物理学报, 2014, 34(1): 39-48.

AN Run-Ling, Kichi-Suke Saito. Lie Derivable Maps on Operator Algebras[J]. Acta mathematica scientia,Series A, 2014, 34(1): 39-48.

[1]	杨丽春, 安润玲. von Neumann代数上的Lie可导映射[J]. 数学物理学报, 2018, 38(5): 864-872.
[2]	崔建莲; 侯晋川. 套代数上保秩一幂零性的可加映射[J]. 数学物理学报, 2007, 27(2): 193-203.