Born Lie algebras
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908358569623552 |
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| author | Gil-García, Alejandro Pilatus, Paula Naomi |
| author_facet | Gil-García, Alejandro Pilatus, Paula Naomi |
| contents | We show that every Born Lie algebra can be obtained by the bicross product construction starting from two pseudo-Riemannian Lie algebras. We then obtain a classification of all Lie algebras up to dimension four and all six-dimensional nilpotent Lie algebras admitting an integrable Born structure. Finally, we study the curvature properties of the pseudo-Riemannian metrics of the integrable Born structures obtained in our classification results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Born Lie algebras Gil-García, Alejandro Pilatus, Paula Naomi Differential Geometry Mathematical Physics Primary 53C15, Secondary 53C50, 53C55, 22E25 We show that every Born Lie algebra can be obtained by the bicross product construction starting from two pseudo-Riemannian Lie algebras. We then obtain a classification of all Lie algebras up to dimension four and all six-dimensional nilpotent Lie algebras admitting an integrable Born structure. Finally, we study the curvature properties of the pseudo-Riemannian metrics of the integrable Born structures obtained in our classification results. |
| title | Born Lie algebras |
| topic | Differential Geometry Mathematical Physics Primary 53C15, Secondary 53C50, 53C55, 22E25 |
| url | https://arxiv.org/abs/2411.04856 |