  We introduce obstructions to the existence of a calibrated G_2-structure on a
Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we
prove that if there is a Lie algebra epimorphism from g to a six-dimensional
Lie algebra h with kernel contained in the center of g, then h has a symplectic
form. As a consequence, we obtain a classification of the nilpotent Lie
algebras that admit a calibrated G_2-structure.

Differential Geometry