Compound-Commuting Mappings on Skew-Hermitian Matrices

Let F be a field with proper involution − and let r, s be even integers with r, s > 2. Let SHr(F) and Cr−1(M) denote the set of all r×r skew-Hermitian matrices over the field F and the (r−1)- th compound of a matrix M, respectively. In this study, we investigate the characterization of a mapping ζ : SHr(F) → SHs(F) that satisfies, ζ(Cr−1(M + γN)) = Cs−1(ζ(M) + γζ(N)), for any M,N ∈ SHr(F) and γ ∈ F−, where F− = {x ∈ F | x = x}.