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 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 ${\mathfrak{g}}^{\prime }$ of codimension 2 and not $J$-invariant, for ${\mathfrak{g}}^{\prime }$ totally real, and for ${\mathfrak{g}}^{\prime }$ of dimension at most 2. This leads to a large part of the full classification for two-step solvable SKT algebras of dimension six.

34 pages; comments are welcome