<p>Preparation: knowledge of basic theory of topological groups and differentiable manifolds. 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.</p>

Mathematics

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College of Letters and Science

The department explores the frontiers of pure and applied mathematical research.

General Catalog

Lie Groups and Lie Algebras

MATH 229B

4 units