Roots of a compact Lie group

2009/08/28 by Tapp, Kristopher
#53C #Differential Geometry (math.DG) #FOS: Mathematics #History and Overview (math.HO)

paper · doi:10.48550/arxiv.0908.4117

Abstract

This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary abstractions. Some familiarity with matrix groups and with maximal tori is assumed. This article is self-contained, but is also intended to serve as a supplemental 10th chapter of an eventual new edition of my textbook, ``Matrix Groups for Undergraduates.''

Related

• Compact groups and their representations
• Representations of Lie groups
• Notes on Chevalley Groups and Root Category II: Compact Lie Groups and Representations
• Sym 'etrie en Physique: Alg `ebres de Lie, Th 'eorie des groupes et\n Repr 'esentations
• Homogeneous Hypercomplex Structures I - the compact Lie groups