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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-1/2 system in a constant quasianti-Hermitian quaternionic potential is considered.doi:10.3842/sigma.2007.088 fatcat:bnm3p5mdzrcclol63zq2e54pgq