Construction of Lie algebras with special G2-structures

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.