A classification of left-invariant symplectic structures on some Lie groups
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866918325245706240 |
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| author | Moscoso, Luis Pedro Castellanos Tamaru, Hiroshi |
| author_facet | Moscoso, Luis Pedro Castellanos Tamaru, Hiroshi |
| contents | We are interested in the classification of left-invariant symplectic structures on Lie groups. Some classifications are known, especially in low dimensions. In this paper we establish a new approach to classify (up to automorphism and scale) left-invariant symplectic structures on Lie groups. The procedure is based on the moduli space of left-invariant nondegenerate $2$-forms. Then we apply our procedure for two particular Lie groups of dimension $2n$ and give classifications of left-invariant symplectic structures on them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_01710 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A classification of left-invariant symplectic structures on some Lie groups Moscoso, Luis Pedro Castellanos Tamaru, Hiroshi Differential Geometry Symplectic Geometry 53C30(Primary), 53D05(Secondary), 22E25(Secondary) We are interested in the classification of left-invariant symplectic structures on Lie groups. Some classifications are known, especially in low dimensions. In this paper we establish a new approach to classify (up to automorphism and scale) left-invariant symplectic structures on Lie groups. The procedure is based on the moduli space of left-invariant nondegenerate $2$-forms. Then we apply our procedure for two particular Lie groups of dimension $2n$ and give classifications of left-invariant symplectic structures on them. |
| title | A classification of left-invariant symplectic structures on some Lie groups |
| topic | Differential Geometry Symplectic Geometry 53C30(Primary), 53D05(Secondary), 22E25(Secondary) |
| url | https://arxiv.org/abs/2012.01710 |