Two-step solvable SKT shears
We use the shear construction to construct and classify a wide range of two-step solvable Lie groups admitting a left-invariant SKT structure. We reduce this to a specification of SKT shear data on Abelian Lie algebras, and which then is studied more deeply in different cases. We obtain classifications and structure results for almost Abelian, for derived algebra of codimension 2 and not J-invariant, for totally real, and for of dimension at most 2. This leads to a large part of the full classification for two-step solvable SKT algebras of dimension six.
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