Complex Projection of Quasianti-Hermitian Quaternionic Hamiltonian Dynamics

We characterize the subclass of quasianti-Hermitian quaternionic Hamiltonian dynamics such that their complex projections are one-parameter semigroup dynamics in the space of complex quasi-Hermitian density matrices. As an example, the complex projection of a spin-$\frac12$ system in a constant quasianti-Hermitian quaternionic potential is considered.