Nonlinear maps preserving Lie products on factor von Neumann algebras

In this paper, we prove that every bijective map preserving Lie products from a factor von Neumann algebra M into another factor von Neumann algebra N is of the form A→ψ(A)+ξ(A), where ψ:M→N is an additive isomorphism or the negative of an additive anti-isomorphism and ξ:M→CI is a map with ξ(AB-BA)=0 for all A,B∈M.