| Additive Lie (ξ-Lie) Derivations and Generalized Lie (ξ-Lie) Derivations on Prime Algebras |
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| 基金项目： | supported by National Natural Science Foundation of China(Grant No.11101250);Youth Foundation of Shanxi Province(Grant No.2012021004);Young Talents Plan for Shanxi University;supported by National Natural Science Foundation of China(Grant No.11171249);Research Fund for the Doctoral Program of Higher Education of China(Grant No.20101402110012);International Cooperation Program in Sciences and Technology of Shanxi Province(Grant No.2011081039) |
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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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| 关 键 词： | Prime algebras ξ-Lie derivations generalized ξ-Lie derivations |
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