2011/10/31 by Marco Freibert, Fabian Schulte-Hengesbach
Mathematics · #math.DG #msc:53C25 #msc:53C15 #msc:53C30
published as Transform. Groups 17 (2012), no. 3, 657 - 689 · 25 pages, v2: minor corrections due to the new classification of the six-dimensional Lie algebras with five-dimensional nilradical by Shabanskaya
arxiv created 2011/11/23 · arxiv updated 2013/02/06
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.