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In this program

Cartan subalgebras and root systems
Weyl group and root reflections
Dynkin diagrams
Classification of simple Lie algebras
Highest weight representations (overview)
Compact Lie groups and maximal tori

Structure theory

Cartan subalgebras and root systems

Lie groups & Lie algebras · Theoretical / proof-based

Topic

Cartan subalgebras and root systems

Practice by unit: Structure theory

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

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