Compact solvmanifolds with calibrated and cocalibrated G2-structures

We give a method to obtain new solvable 7-dimensional Lie algebras endowed with closed and coclosed G(2)-structures starting from 6-dimensional solvable Lie algebras with symplectic half-flat and half-flat SU(3)-structures, respectively. Provided the existence of a lattice for the corresponding Lie groups we obtain new examples of compact solvmanifolds endowed with calibrated and cocalibrated G(2)-structures. As an application of this construction we also obtain a formal compact solvmanifold with first Betti number b(1) = 1 endowed with a calibrated G(2)-structure and such that does not admit any invariant torsion-free G(2)-structure.