Abstract
In this chapter we will give a quick introduction to the theory of Lie groupoids, and then present some normal form theorems for Lie groupoids and symplectic groupoids in the proper case. For a more comprehensive introduction, the reader may consult other references, in particular the book by Mackenzie [228], and also [60, 254].
The relations between Lie groupoids and Poisson structures will become clear near the end of this chapter when we discuss symplectic groupoids, and in Chapter 8 where it is shown that Lie algebroids, i.e., the infinitesimal versions of Lie groupoids, are nothing but fiber-wise linear Poisson manifolds.
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© 2005 Birkhäuser Verlag
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(2005). Lie Groupoids. In: Bass, H., Oesterlé, J., Weinstein, A. (eds) Poisson Structures and Their Normal Forms. Progress in Mathematics, vol 242. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7335-0_7
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DOI: https://doi.org/10.1007/3-7643-7335-0_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7334-4
Online ISBN: 978-3-7643-7335-1
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