Roots of a compact Lie group

TL;DR

This paper provides an elementary, example-driven introduction to the concept of roots in compact Lie groups, aiming to make the topic accessible to undergraduates and supplement existing textbooks.

Contribution

It offers a simplified, self-contained exposition on roots in compact Lie groups, emphasizing clarity and examples over abstract generality.

Findings

Clear explanation of roots in compact Lie groups

Accessible approach for undergraduates

Self-contained exposition suitable as supplementary material

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.''