Fall 2022

Lie Groups/Lie Algebras

Listed in: Mathematics and Statistics, as MATH-405


Ivan Contreras (Section 02)


Lie groups and Lie algebras appear naturally in the study of symmetries of geometric objects. Lie algebras carry local information and can be studied using tools from linear algebra. Finite dimensional Lie groups can be constructed using techniques from calculus and group theory.

This course serves as a first introduction to Lie groups and Lie algebras. We will examine the structure of finite dimensional matrix Lie groups, the exponential and differentiation maps, as well as compact Lie groups. We will also study Lie algebras, ideals and homomorphisms, nilpotent and solvable Lie algebras, Cartan subalgebras, semisimplicity and root systems, and the classification of semisimple Lie algebras. This classification is not only a fundamental result in Lie Theory, but is also an archetype of classifications that appear in other areas of math. More amazingly, this classification is embodied in simple combinatorial pictures called Dynkin diagrams, which underlie surprisingly disparate fields, such as geometric group theory, quiver representation theory, and string theory. Four class meetings per week.

MATH 405 - LEC

Section 02
M 10:00 AM - 10:50 AM SMUD 014
W 10:00 AM - 10:50 AM SMUD 014
F 10:00 AM - 10:50 AM SMUD 014

ISBN Title Publisher Author(s) Comment Book Store Price
Naive Lie Theory, Undergraduate Texts in Mathematics Springer 2008 Stillwell, John TBD


2023-24: Not offered
Other years: Offered in Fall 2022, Spring 2025