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arXiv · 2404.10607

Transitive Lie algebroids and \textbf{Q}-manifolds

Daniel Beltita·Fernand Pelletier
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Abstract

We introduce the notions of locally trivial \textbf{Q}-groupoid and principal \textbf{Q}-bundle, which are the appropriate versions of locally trivial Lie groupoids and principal fibre bundles in the framework of R. Barre's \textbf{Q}-manifolds. As an application, we prove that every transitive Lie algebroid over a second countable, smooth manifold arises from the Atiyah sequence of a certain principal \Q-bundle. Consequently, transitive Lie algebroids over second countable, smooth manifolds are integrated to locally trivial \textbf{Q}-groupoids.

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Daniel Beltita, Fernand Pelletier. 2026-06-22. Transitive Lie algebroids and \textbf{Q}-manifolds. https://arxiv.org/abs/2404.10607

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