Two-step solvable SKT shears

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