Half-flat SU(3)-structures are the natural initial values for Hitchin's
evolution equations whose solutions define parallel G_2-structures. Together
with the results of arXiv:0912.3486v1, the results of this article completely
solve the existence problem of left-invariant half-flat SU(3)-structures on
decomposable Lie groups. The proof is supported by the calculation of the Lie
algebra cohomology for all indecomposable five-dimensional Lie algebras which
refines and clarifies the existing classification of five-dimensional Lie
algebras.Comment: 15 pages, v2: minor corrections and improved presentatio