Lie Groups and Lie Algebras II
MIT OpenCourseWare offers the second half of this graduate-level sequence, continuing from Lie Groups and Lie Algebras I. Topics covered include classical groups, Haar measure on locally compact groups, the representation-theoretic treatment of the hydrogen atom, representations of compact and finite groups, and a full proof of the Peter-Weyl theorem. The course goes on to maximal tori, Cartan and Iwasawa decompositions, and the classification of real reductive Lie groups, along with the topology of Lie groups, a proof of the third fundamental theorem of Lie theory, Levi decomposition, Ado's theorem, Borel subgroups, and flag manifolds. Materials consist of MIT's standard OCW course site, including syllabus and readings, under a Creative Commons license, with no certificate offered. This is dense graduate mathematics aimed at students with a solid grounding in algebra and topology.