  The study of quasi-K\"ahler Chern-flat almost Hermitian manifolds is strictly
related to the study of anti-bi-invariant almost complex Lie algebras. In the
present paper we show that quasi-K\"ahler Chern-flat almost Hermitian
structures on compact manifolds are in correspondence to complex parallelisable
Hermitian structures satisfying the second Gray identity. From an algebraic
point of view this correspondence reads as a natural correspondence between
anti-bi-invariant almost complex structures on Lie algebras to bi-invariant
complex structures. Some natural algebraic problems are approached and some
exotic examples are carefully described.
