Group actions on $p$-adic symplectic manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917152048545792 |
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| author | Crespo, Luis Pelayo, Álvaro |
| author_facet | Crespo, Luis Pelayo, Álvaro |
| contents | Let $p$ be a prime number. We introduce symplectic actions of $p$-adic analytic Lie groups on $p$-adic symplectic manifolds. Then we show that any $p$-adic symplectic action $G\times(M,ω)\to(M,ω)$ has a momentum map $μ:M\to\mathfrak{g}^*$, and that a proper $p$-adic symplectic action is Hamiltonian if and only if every orbit is isotropic. We conclude by defining $p$-adic symplectic toric manifolds, by analogy with the real case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15575 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Group actions on $p$-adic symplectic manifolds Crespo, Luis Pelayo, Álvaro Symplectic Geometry Mathematical Physics Let $p$ be a prime number. We introduce symplectic actions of $p$-adic analytic Lie groups on $p$-adic symplectic manifolds. Then we show that any $p$-adic symplectic action $G\times(M,ω)\to(M,ω)$ has a momentum map $μ:M\to\mathfrak{g}^*$, and that a proper $p$-adic symplectic action is Hamiltonian if and only if every orbit is isotropic. We conclude by defining $p$-adic symplectic toric manifolds, by analogy with the real case. |
| title | Group actions on $p$-adic symplectic manifolds |
| topic | Symplectic Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2512.15575 |