Half-flat structures on indecomposable Lie groups |
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Authors: | Marco Freibert Fabian Schulte-Hengesbach |
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Affiliation: | 1. Fachbereich Mathematik, Universit?t Hamburg, Bundesstr. 55, 20146, Hamburg, Germany
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Abstract: | This article can be viewed as a continuation of the articles [SH] and [FS] in which 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 nilradicals 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 nilradicals is established. Additionally, it is proved that all non-solvable six-dimensional Lie algebras admit half-flat SU(3)-structures. |
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