Closed G$_2$-structures on unimodular Lie algebras with non-trivial center
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916547970203648 |
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| author | Fino, Anna Raffero, Alberto Salvatore, Francesca |
| author_facet | Fino, Anna Raffero, Alberto Salvatore, Francesca |
| contents | We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G$_2$-structure. Using this result, we classify all unimodular Lie algebras with non-trivial center admitting closed G$_2$-structures, up to isomorphism, and we show that six of them arise as the contactization of a symplectic Lie algebra. Finally, we prove that every semi-algebraic soliton on the contactization of a symplectic Lie algebra must be expanding, and we determine all unimodular Lie algebras with center of dimension at least two that admit semi-algebraic solitons, up to isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_11628 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Closed G$_2$-structures on unimodular Lie algebras with non-trivial center Fino, Anna Raffero, Alberto Salvatore, Francesca Differential Geometry We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G$_2$-structure. Using this result, we classify all unimodular Lie algebras with non-trivial center admitting closed G$_2$-structures, up to isomorphism, and we show that six of them arise as the contactization of a symplectic Lie algebra. Finally, we prove that every semi-algebraic soliton on the contactization of a symplectic Lie algebra must be expanding, and we determine all unimodular Lie algebras with center of dimension at least two that admit semi-algebraic solitons, up to isomorphism. |
| title | Closed G$_2$-structures on unimodular Lie algebras with non-trivial center |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2103.11628 |