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arXiv · 1712.09664

Closed G$_2$-structures on non-solvable Lie groups

Anna Fino·Alberto Raffero
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Abstract

We investigate the existence of left-invariant closed G$_2$-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a structure exists only when the semisimple part is isomorphic to $\mathfrak{sl}(2,\mathbb{R})$ and the radical is unimodular and centerless. Moreover, we classify unimodular Lie algebras with non-trivial Levi decomposition admitting closed G$_2$-structures.

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Anna Fino, Alberto Raffero. 2017-12-27. Closed G$_2$-structures on non-solvable Lie groups. https://doi.org/10.1007/s13163-019-00296-0

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