Algebroid Desingularizable Poisson Structures
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866918516505968640 |
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| author | Rankin, Shane |
| author_facet | Rankin, Shane |
| contents | We introduce algebroid desingularizable Poisson manifolds, a class of Poisson manifolds induced by symplectic Lie algebroids with almost-injective anchors, generalizing structures including log-symplectic, $b^m$-symplectic, $E$-symplectic manifolds, and hypersurface algebroids. We show that the dual of real, finite-dimensional, non-abelian, reductive Lie algebras never admit such algebroids. We finish by giving two infinite families of $2$-step nilpotent Lie algebras, one of which is desingularizable, and one of which is not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22519 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebroid Desingularizable Poisson Structures Rankin, Shane Differential Geometry Symplectic Geometry We introduce algebroid desingularizable Poisson manifolds, a class of Poisson manifolds induced by symplectic Lie algebroids with almost-injective anchors, generalizing structures including log-symplectic, $b^m$-symplectic, $E$-symplectic manifolds, and hypersurface algebroids. We show that the dual of real, finite-dimensional, non-abelian, reductive Lie algebras never admit such algebroids. We finish by giving two infinite families of $2$-step nilpotent Lie algebras, one of which is desingularizable, and one of which is not. |
| title | Algebroid Desingularizable Poisson Structures |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2605.22519 |