Maps Preserving \([[G,S],T]_{\diamond }\) on Factor von Neumann Algebras

Let \({\mathcal {M}}\) $\mathcal{M}$ and \({\mathcal {N}}\) $\mathcal{N}$ be factor von Neumann algebras, and let \(\Psi :{\mathcal {M}}\rightarrow {\mathcal {N}}\) $\mathrm{\Psi }:\mathcal{M}\to \mathcal{N}$ be a bijective map preserving \([[G,S],T]_{\diamond }.\) ${[[G,S],T]}_{\diamond }.$ In this paper, we will study the characterization of this map when \({\textrm{dim}} {\mathcal {M}}>1.\) $\text{dim}\mathcal{M}>1.$