Math 577/578/579
Lie Groups and Lie Algebras

Eric Babson (577), Gerald Folland(578/579)

Autumn 2005 (M/W/F 2:30); Winter 2006/Spring 2006 (M/W/F 9:30),

This will be an introductory course on the classification and representation theory of semisimple Lie algebras in Autumn (577) followed by Lie groups and their representations, with emphasis on the analytic side of the theory in Winter and Spring (578-9).

Texts Introduction to Lie Algebras and Representation Theory by James Humphreys for 577, and Lie Groups: An Introduction through Linear Groups by Wulf Rossmann (probably supplemented by other materials in the spring) for 578-9.

Prerequisites: Algebraic background for 577-9: a familiarity with linear algebra and the rudiments of group theory (Math 506 is not necessary). Analytic/geometric background for 578-9: Math 544-5-6 taken concurrently or previously. It is possible (though not really desirable) to take 578-9 without having taken 577 if you're willing to accept a few theorems on faith.