Intro to Lie Algebras

Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo

“Semisimple Lie Algebras”

Root spaces are a generalization of eigenspaces, and it turns out that a semisimple Lie algebra can be recovered by its roots. We’ll look at the so-called root space decomposition, and also observe some nice things about the simple algebra sl(2,C) and its irreducible modules.