The red dots are the 24 roots of D4, projected from 4 dimensions down to 3 and then drawn in the plane.
These points are the vertices of the 24-cell, whose edges are also drawn here.

Seminar - Fall 2008

Lie Theory Through Examples

John Baez

Simple Lie groups and Lie algebras tie together some of the most beautiful, symmetrical structures in mathematics: Platonic solids and their higher-dimensional cousins, finite groups generated by reflections, lattice packings of spheres, incidence geometries, symmetric spaces, and more. In this fall's seminar we'll explore this web of ideas through examples, starting with easy 'classical' ones and working up to 'exceptional' ones such as the 248-dimensional Lie group E8.

Here are the lecture notes, and blog entries where you can ask questions and discuss ideas:

If you discover any errors in the course notes please email me, and I'll try to correct them. I'll keep a list of errors that haven't been fixed yet.

You can also download LaTeX files of the lecture notes, if for some bizarre reason you want them. However, the authors keep all rights to this work, except when stated otherwise.
© 2008 John Baez