Closed G$_2$-structures on non-solvable Lie groups
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866917882799063040 |
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| author | Fino, Anna Raffero, Alberto |
| author_facet | Fino, Anna Raffero, Alberto |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1712_09664 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Closed G$_2$-structures on non-solvable Lie groups Fino, Anna Raffero, Alberto Differential Geometry 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. |
| title | Closed G$_2$-structures on non-solvable Lie groups |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1712.09664 |