Abstract
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 mathfrak {g} almost Abelian, for derived algebra mathfrak {g}' of codimension 2 and not J-invariant, for mathfrak {g}' totally real, and for mathfrak {g}' 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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