  We present a new simple proof of the fact that certain group manifolds as
well as certain homogeneous spaces G/H of dimension 4n admit a quaternionic
triple of integrable complex structures that are covariantly constant with
respect to the same torsionful Bismut connection, i.e. exhibit the HKT
geometry. The key observation is that different complex structures are
interrelated by automorphisms of the Lie algebra. To construct the quaternion
triples, one only needs to construct the proper automorphisms, which is a more
simple problem.
