Abstract
We classify six-dimensional Lie groups which admit a left-invariant half-flat SU(3)-structure and which split in a direct product of three-dimensional factors. Moreover, a complete list of those direct products is obtained which admit a left-invariant half-flat SU(3)-structure such that the three-dimensional factors are orthogonal. Similar classification results are proved for left-invariant half-flat SL(3,R)-structures on direct products with either definite and orthogonal or isotropic factors.
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