Nonlinear Maps Preserving Mixed Product on Factors

Let A and B be two factors with dimA 4. In this article, it is proved that a bijective map Φ:A→B satisfies Φ([A∙B,C])=[Φ(A)∙Φ(B),Φ(C)] for all A,B,C∈A if and only if Φ is a linear ∗-isomorphism, or a conjugate linear ∗-isomorphism, or the negative of a linear ∗-isomorphism, or the negative of a conjugate linear ∗-isomorphism.