Abstract
We inquire the motion of charged particles varying under the effect of Lorentz force produced by magnetic and Killing magnetic fields in anti-de Sitter 3-space . Primarily, we characterize magnetic trajectories in
in terms of their Frenet apparatus. Thereafter, utilizing a geometrical model of split-quaternions for
(where
corresponds to a subspace of the Lie group H of split-quaternions) we find 6 independent unit Killing vector fields on
which constitutes a basis for the corresponding 6D Lie algebra i(
). We conclude with characterizations of Killing magnetic trajectories in
with respect to quasi-slope, curvature and torsion or pseudo-torsion (depending on the situation).