SKT solvable Lie algebras with codimension two nilradical

TL;DR

This paper classifies six-dimensional SKT solvable Lie algebras with codimension two nilradicals, providing constructions to extend nilpotent cases and producing new examples of SKT and generalized Kähler compact solvmanifolds.

Contribution

It offers a classification of six-dimensional SKT solvable Lie algebras with codimension two nilradicals and introduces methods to extend nilpotent SKT algebras to higher dimensions.

Findings

Classification of six-dimensional SKT solvable Lie algebras

Construction method for extending nilpotent SKT algebras

New examples of SKT and generalized Kähler compact solvmanifolds

Abstract

In the present paper we study SKT and generalized K\"ahler structures on solvable Lie algebras with (not necessarily abelian) codimension two nilradical. We treat separately the case of $J$-invariant nilradical and non $J$-invariant nilradical. A classification of such SKT Lie algebras in dimension six is provided. In particular, we give a general construction to extend SKT nilpotent Lie algebras to SKT solvable Lie algebras of higher dimension, and we construct new examples of SKT and generalized K\"ahler compact solvmanifolds.