Singular subalgebroids

2018/05/07 by Marco Zambon, Zambon, Marco, Iakovos Androulidakis +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1805.02480

openalex publication_date 2018/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce singular subalgebroids of an integrable Lie algebroid, extending the notion of Lie subalgebroid by dropping the constant rank requirement. We lay the bases of a Lie theory for singular subalgebroids: we construct the associated holonomy groupoids, adapting the procedure of Androulidakis-Skandalis for singular foliations, in a way that keeps track of the choice of Lie groupoid integrating the ambient Lie algebroid. The holonomy groupoids are topological groupoids, and are suitable for noncommutative geometry as they allow for the construction of the associated convolution algebras. Further we carry out the construction for morphisms in a functorial way.

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