Algebroid Desingularizable Poisson Structures

Fuente: arXiv
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Autore principale: Rankin, Shane
Natura: Preprint
Pubblicazione: 2026
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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