On the geometry and cohomology of almost abelian solvmanifolds

We study left-invariant generalized complex structures on almost abelian Lie groups $G_A = \mathbb{R} \ltimes_{e^{tA}} \mathbb{R}^{d}$, and on the associated solvmanifolds. Our starting point is that the $\mathbf{i}$-eigenspace $\mathfrak{L}$ of such a structure is itself an almost abelian complex L