This work focuses on characterizing structure-preserving maps between factor von Neumann algebras with respect to a class of mixed skew Lie–Jordan \(n\) -products. Specifically, we consider expressions of the form \( [A_1, A_2]_*\circ A_3 \circ \cdots \circ A_n, \) where each \(A_i \in \mathfrak {S}\) and \(\mathfrak {S}\) is a factor von Neumann algebra. Here, the skew Lie product is defined by \([A_1, A_2]_*= A_1A_2 - A_2^*A_1\) , and the Jordan product by \(A_1 \circ A_2 = A_1A_2 + A_2A_1\) . We prove that any map preserving these mixed products is necessarily a linear \(*\) -isomorphism.
