Half-flat structures on decomposable Lie groups (Q430784)
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scientific article; zbMATH DE number 6050326
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Half-flat structures on decomposable Lie groups |
scientific article; zbMATH DE number 6050326 |
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Half-flat structures on decomposable Lie groups (English)
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26 June 2012
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Half-flat \(\mathrm{SU}(3)\)-structures are the natural initial values for Hitchin's evolution equations whose solutions define parallel \(G_{2}\)-structures. Together with the results of \textit{F. Schulte-Hengesbach} [J. Geom. Phys. 60, No. 11, 1726--1740 (2010; Zbl 1246.53073)], the results of this article completely solve the existence problem of left-invariant half-flat \(\mathrm{SU}(3)\)-structures on decomposable Lie groups. The proof is supported by the calculation of the Lie algebra cohomology for all indecomposable five-dimensional Lie algebras, which refines and clarifies the existing classification of five-dimensional Lie algebras.
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Lie groups
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\(G_2\)-structure
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decomposable Lie group
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