算子代数上的Lie可导映射

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r: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.

Lie Derivable Maps on Operator Algebras

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.