MATH 229ALie Groups and Lie Algebras
Mathematics · 4 units · Graduate courses (200-299)
Lie groups, Lie algebras, subgroups, subalgebras. Exponential map. Universal enveloping algebra. Campbell/Hausdorff formula. Nilpotent and solvable Lie algebras. Cohomology of Lie algebras. Theorems of Weyl, Levi-Mal’cev. Semi-simple Lie algebras. Classification of simple Lie algebras. Representations. Compact groups. Weyl character formula.
When it runs
- Fall 2025
- Fall 2026
Scheduled, not typical — from UCLA’s Schedule of Classes, which publishes Fall 2025 through Spring 2027 and nothing before it.
Requisites
Official UCLA wording
Preparation: knowledge of basic theory of topological groups and differentiable manifolds.
BruinTree reads · Preparation
needs reviewconfidence 0.00 · from textBruinTree could not read this requirement — see UCLA’s wording above.
- · could not read "knowledge of basic theory of topological groups" (no course number found)
- · could not read "differentiable manifolds" (no course number found)
- · no course reference could be read from this requisite
Requires
Everything that has to come before this course, not just the courses named in the requisite above.
Nothing — this is an entry point.
Unlocks
What this course is a requisite for, and what those courses lead to in turn.
No course in the catalog lists this as a requisite.