Abstract
The examples from Chapter 17 show that many geometrically defined Lie groups have several connected components. While only the connected component of the identity is accessible to the methods built on the exponential function, there are still tools to analyze nonconnected Lie groups. In the present chapter, we present some of these tools. The key notion is that of an extension of a discrete group by a (connected) Lie group.
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Notes
- 1.
The subscript AS refers to Alexander–Spanier because this differential leads to the Alexander–Spanier cohomology in algebraic topology.
References
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Hilgert, J., Neeb, KH. (2012). Nonconnected Lie Groups. In: Structure and Geometry of Lie Groups. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-84794-8_18
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DOI: https://doi.org/10.1007/978-0-387-84794-8_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-84793-1
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