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arXiv · 2011.04331

Two-step solvable SKT shears

Marco Freibert·Andrew Swann
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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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Marco Freibert, Andrew Swann. 2020-11-09. Two-step solvable SKT shears. https://arxiv.org/abs/2011.04331

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