Abstract
Since a compact Lie group, G, can be thought of as a Lie subgroup of U(n), Theorems 3.28 and 2.15, it is possible to diagonalize each g ∃ G using conjugation in U(n). In fact, the main theorem of this chapter shows it is possible to diagonalize each g ∃ G using conjugation in G. This result will have far-reaching consequences, including various structure theorems.
This is a preview of subscription content, log in via an institution to check access.
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
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
(2007). Abelian Lie Subgroups and Structure. In: Sepanski, M.R. (eds) Compact Lie Groups. Graduate Texts in Mathematics, vol 235. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49158-5_5
Download citation
DOI: https://doi.org/10.1007/978-0-387-49158-5_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-30263-8
Online ISBN: 978-0-387-49158-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)