Weak embeddings of generalized hexagons and groups of type G2

In this note we give two characterizations of the natural embedding of the classical G2(L)-hexagon in a projective space P(V), where V is a 7-dimensional (or 6-dimensional in case the characteristic of L is 2) vector-space over an extension skew field of L. We use these geometric results to characterize this vector-space V as a G2(L)-module on which the long root subgroups of G2(L) act quadratically with 2-dimensional commutator space.