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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Editor information
Rights and permissions
Copyright information
© 2005 Birkhäuser Verlag
About this chapter
Cite this chapter
(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
Download citation
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
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)