In this program
- Lie groups: definitions, examples (GL(n), SO(n), SU(n))
- Lie algebras: bracket, homomorphisms, and ideals
- Exponential map
- Baker–Campbell–Hausdorff formula (introduction)
- Adjoint representation and Killing form
- Semisimple and simple Lie algebras
Lie groups and Lie algebras
Lie groups: definitions, examples (GL(n), SO(n), SU(n))
Lie groups & Lie algebras · Theoretical / proof-based
Topic
Lie groups: definitions, examples (GL(n), SO(n), SU(n))
Graduate Lie Groups & Lie Algebras — scope drawn from open Lie theory notes and typical US graduate Lie groups syllabi.