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.

我们使用剪切构造来构造和分类允许左不变SKT结构的两步可解Lie组。我们将其简化为关于Abelian Lie代数的SKT剪切数据的规范，然后在不同情况下进行更深入的研究。我们获得用于分类和结构的结果\（\ mathfrak {G} \）几乎阿贝尔，派生代数\（\ mathfrak {G} '\）余维2的和不Ĵ -invariant，对于\（\ mathfrak {G}' \）完全真实，并且维数最大为\（\ mathfrak {g}'\）。这导致了维数为两步的可解SKT代数的完整分类的很大一部分。