Ad-invariant metrics on nonnice nilpotent Lie algebras
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929306573209600 |
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| author | Conti, Diego del Barco, Viviana Rossi, Federico A. |
| author_facet | Conti, Diego del Barco, Viviana Rossi, Federico A. |
| contents | We proved in previous work that all real nilpotent Lie algebras of dimension up to $10$ carrying an ad-invariant metric are nice. In this paper we show by constructing explicit examples that nonnice irreducible nilpotent Lie algebras admitting an ad-invariant metric exist for every dimension greater than $10$ and every nilpotency step greater than $2$. In the way of doing so, we introduce a method to construct Lie algebras with ad-invariant metrics called the single extension, as a parallel to the well-known double extension procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_11274 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Ad-invariant metrics on nonnice nilpotent Lie algebras Conti, Diego del Barco, Viviana Rossi, Federico A. Differential Geometry 17B30 (Primary) 53C30, 53C50, 17B01 (Secondary) We proved in previous work that all real nilpotent Lie algebras of dimension up to $10$ carrying an ad-invariant metric are nice. In this paper we show by constructing explicit examples that nonnice irreducible nilpotent Lie algebras admitting an ad-invariant metric exist for every dimension greater than $10$ and every nilpotency step greater than $2$. In the way of doing so, we introduce a method to construct Lie algebras with ad-invariant metrics called the single extension, as a parallel to the well-known double extension procedure. |
| title | Ad-invariant metrics on nonnice nilpotent Lie algebras |
| topic | Differential Geometry 17B30 (Primary) 53C30, 53C50, 17B01 (Secondary) |
| url | https://arxiv.org/abs/2111.11274 |