Additive Lie (ξ-Lie) derivations and generalized Lie (ξ-Lie) derivations on prime algebras

被引：0
作者：
Xiao Fei Qi
Jin Chuan Hou
机构：
[1] Shanxi University,Department of Mathematics
[2] Taiyuan University of Technology,Department of Mathematics
来源：
Acta Mathematica Sinica, English Series | 2013年 / 29卷
关键词：
Prime algebras; -Lie derivations; generalized ; -Lie derivations; 47L35; 16W25;
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摘要：
The additive (generalized) ξ-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumptions, that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) ξ-Lie derivation with ξ ≠1 if and only if it is an additive (generalized) derivation satisfying L(ξA) = ξL(A) for all A. These results are then used to characterize additive (generalized) ξ-Lie derivations on several operator algebras such as Banach space standard operator algebras and von Neumman algebras.
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页码：383 / 392
页数：9
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