  We give a method to obtain new 7-dimensional Lie algebras endowed with closed
and coclosed G2-structures starting from 6-dimensional Lie algebras with
symplectic half- at SU(3)-structures and half- at SU(3)- structures,
respectively. Finally, we describe all the 7-dimensional Lie algebras with a
closed G2-structure that are obtained with this method from the 6-dimensional
solvable Lie algebras admitting a symplectic half- at SU(3)- structure.
