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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

Adjoint representation and Killing form

Lie groups & Lie algebras · Theoretical / proof-based

Topic

Adjoint representation and Killing form

Practice by unit: Lie groups and Lie algebras

Graduate Lie Groups & Lie Algebras — scope drawn from open Lie theory notes and typical US graduate Lie groups syllabi.

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