English

Half-flat structures on indecomposable Lie groups

Differential Geometry 2013-02-06 v2

Abstract

This article can be viewed as a continuation of the articles arXiv:0912.3486 and arXiv:1012.3714 where the decomposable Lie algebras admitting half-flat SU(3)-structures are classified. The new main result is the classification of the indecomposable six-dimensional Lie algebras with five-dimensional nilradical which admit a half-flat SU(3)-structure. As an important step of the proof, a considerable refinement of the classification of six-dimensional Lie algebras with five-dimensional non-Abelian nilradical is established. Additionally, it is proved that all non-solvable six-dimensional Lie algebras admit half-flat SU(3)-structures.

Keywords

Cite

@article{arxiv.1110.1512,
  title  = {Half-flat structures on indecomposable Lie groups},
  author = {Marco Freibert and Fabian Schulte-Hengesbach},
  journal= {arXiv preprint arXiv:1110.1512},
  year   = {2013}
}

Comments

25 pages, v2: minor corrections due to the new classification of the six-dimensional Lie algebras with five-dimensional nilradical by Shabanskaya

R2 v1 2026-06-21T19:16:40.633Z