This course is designed to be an introduction to the topic of Lie algebras. Although Lie algebras have connections to harmonic analysis and differential geometry, the approach here will be algebraic. Beyond studying the basic definitions and concepts, we will also focus on the structure of Lie algebras, their classification, and representation theory. There will be an emphasis on concrete classical examples such as \(gl_n\), \(sl_n\), \(sp_n\) and \(so_n\). Besides Fulton and Harris, Representation Theory, A First Course, (originally published by Springer in 1991), which is the main textbook for the course, I also recommend reading:
* J. Humphreys, Introduction to Lie algebras and Representation theory Graduate Texts in Math, v. 9, published by Springer, 1973;
* J. Stillwell Naive Lie Theory Undergraduate Texts in Math, 2010; and
* R. Howe "Very basic Lie theory" November 1983, Math Monthly.
Fulton and Harris, Representation Theory, A First Course, Springer