Abstract
The idea of a groupoid is a generalization of that of a group, where not every pair of elements can be combined. In this chapter we review the concepts of Lie groupoid and Lie algebroid.
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Notes
- 1.
We shall often write the source of a typical groupoid element as \({\tilde{x}}\) and the target as x. This choice is deliberate, and is related to our use, when considering the Lie algebroid of a Lie groupoid, of vector fields vertical over the source projection \(\alpha \).
- 2.
There are different conventions in the literature regarding the direction of trivialization maps. We shall consistently regard the trivial (product) manifold as the domain of the trivialization map rather than the codomain, as this simplifies many formulæ.
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Crampin, M., Saunders, D. (2016). Lie Groupoids and Lie Algebroids. In: Cartan Geometries and their Symmetries. Atlantis Studies in Variational Geometry, vol 4. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-192-5_1
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DOI: https://doi.org/10.2991/978-94-6239-192-5_1
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Publisher Name: Atlantis Press, Paris
Print ISBN: 978-94-6239-191-8
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