Nonlinear maps preserving mixed Lie triple products on factor von Neumann algebras

Abstract

We prove that every bijective map that preserves mixed Lie triple products from a factor von Neumann algebra M with dimM>4 into another factor von Neumann algebra N is of the form A→ϵΨ(A), where ϵ∈{1,−1} and Ψ:M→N is a linear ∗-isomorphism or a conjugate linear ∗-isomorphism. Also, we give the structure of this map when dimM=4.