A Hilbert--Mumford criterion for nilsolitons
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918207229526016 |
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| author | Hashimoto, Yoshinori |
| author_facet | Hashimoto, Yoshinori |
| contents | We give an algebraic criterion for a nilpotent real Lie algebra and prove that it provides a necessary and sufficient condition for the associated nilpotent Lie group to admit left-invariant Ricci solitons, called nilsolitons. As an application of this result, we generalise Nikolayevsky's criterion for the existence of nilsolitons to nilpotent Lie algebras without nice bases. We further prove a modified version of the Taketomi--Tamaru conjecture for nilpotent Lie groups which gives an obstruction to the existence of nilsolitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12469 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Hilbert--Mumford criterion for nilsolitons Hashimoto, Yoshinori Differential Geometry Algebraic Geometry 53C30 (Primary), 22E25 (Secondary) We give an algebraic criterion for a nilpotent real Lie algebra and prove that it provides a necessary and sufficient condition for the associated nilpotent Lie group to admit left-invariant Ricci solitons, called nilsolitons. As an application of this result, we generalise Nikolayevsky's criterion for the existence of nilsolitons to nilpotent Lie algebras without nice bases. We further prove a modified version of the Taketomi--Tamaru conjecture for nilpotent Lie groups which gives an obstruction to the existence of nilsolitons. |
| title | A Hilbert--Mumford criterion for nilsolitons |
| topic | Differential Geometry Algebraic Geometry 53C30 (Primary), 22E25 (Secondary) |
| url | https://arxiv.org/abs/2311.12469 |