# Visualizing Lie Subalgebras using Root and Weight Diagrams

Author(s):
Tevian Dray (Oregon State Univ.) and Aaron Wangberg (Winona State Univ.)

## Abstract

While Dynkin diagrams are useful for classifying Lie algebras, it is the root and weight diagrams that are most often used in applications, such as when describing the properties of fundamental particles. This paper illustrates how to construct root and weight diagrams from Dynkin diagrams, and how the root and weight diagrams can be used to identify subalgebras. In particular, we show how this can be done for some algebras whose root and weight diagrams have dimension greater than 3, including the exceptional Lie algebras $$F_4$$ and $$E_6$$.

## Contents

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###### Published February 2009. © 2009 Aaron Wangberg and Tevian Dray.

Tevian Dray (Oregon State Univ.) and Aaron Wangberg (Winona State Univ.), "Visualizing Lie Subalgebras using Root and Weight Diagrams," Loci (February 2010), DOI:10.4169/loci003287