广义矩阵代数上的非线性Lie中心化子
Nonlinear Lie centralizers of generalized matrix algebras

摘要： 令G是广义矩阵代数。若Ф:G→G是非线性Lie中心化子, 在一些微弱的假设下, 得Ф=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。
Abstract: Let G be a generalized matrix algebra. Assume that Ф:G→Gis a nonlinear Lie centralizer. It is shown that, under some mild conditions, Ф can be expressed as Ф=φ+τ, where φ:G→Gis 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