Isotropic Trialitarian Algebraic Groups

By modifying a construction from Knuset al., we construct all isotropic algebraic groups of type3D4and6D4over an arbitrary field of characteristic ≠ 2. We also provide a nice isomorphism criterion for such groups. The results of this paper extend the main results of Allison (using entirely different methods) to fields of nonzero characteristic and algebraic groups.