Theoretical / proof-based
Lie groups & Lie algebras · Graduate · Math
Topics
Lie groups and Lie algebras
- Lie groups: definitions, examples (GL(n), SO(n), SU(n))
- Lie algebras: bracket, homomorphisms, and ideals
- Exponential map and Baker–Campbell–Hausdorff formula (introduction)
- Adjoint representation and Killing form
- Semisimple and simple Lie algebras
Structure theory
- Cartan subalgebras and root systems
- Weyl group and root reflections
- Dynkin diagrams and classification of simple Lie algebras
- Highest weight representations (overview)
- Compact Lie groups and maximal tori
Advanced topics
- Universal enveloping algebras (introduction)
- Haar measure and integration on compact groups
- Symmetric spaces (preview)
- Lie cohomology (optional)
- Applications to differential geometry and physics
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$1,162 · Lie groups & Lie algebras · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.