Abelianization of Lie algebroids and Lie groupoids
Shuyu Xiao
TL;DR
This paper explores the process of abelianization for Lie algebroids and groupoids, establishing conditions for their existence in various categories, thereby advancing understanding of their structural properties.
Contribution
It provides necessary and sufficient conditions for the abelianization of Lie algebroids and groupoids in smooth and diffeological categories, respectively.
Findings
Established a criterion for abelianization of Lie algebroids.
Provided sufficient conditions for abelianization of groupoids in the smooth category.
Derived necessary and sufficient conditions for groupoid abelianization in the diffeological category.
Abstract
We investigate the abelianization of a Lie algebroid and provide a necessary and sufficient condition for its existence. We also study the abelianization of groupoids and provide sufficient conditions for its existence in the smooth category and a necessary and sufficient condition for its existence in the diffeological category.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology