广义矩阵代数上的非线性Lie中心化子

Nonlinear Lie centralizers of generalized matrix algebras

令G是广义矩阵代数。若φ:G→G是非线性Lie中心化子,在一些微弱的假设下,得φ=φ+τ,其中φ:G→G是可加的中心化子,τ:G→Z(G)对所有x,y∈G,满足τ[x,y]=0。作为应用,获得了因子von Neumann代数、三角代数上非线性Lie中心化子的刻画。

Let G be a generalized matrix algebra. Assume that φ： G→G is a nonlinear Lie centralizer. It is shown that,under some mild conditions,φ can be expressed as φ = φ ＋ τ,where φ： G→G is an additive centralizer and τ：G →Z（ G） is a mapping that vanishes at commutators. Based on the above results,the characterizations of nonlinear Lie centralizers on factor von Neumann algebras,triangular algebras are obtained.