Course Syllabus

Lecture Content Reading
1 Recollections on smooth manifolds, Lie groups Etingof Ch. 1–2
2 Covering spaces of Lie groups, actions Etingof Ch. 3–4
3 Classical Lie groups Etingof Ch. 6
4 Tangent bundle, Lie algebra, exponential map Etingof Ch. 5, 7–8
5 Fundamental theorems of Lie theory, I Etingof Ch. 9–10
6 Fundamental theorems of Lie theory, II Etingof Ch. 9–10
7 Representations  Etingof Ch. 11
8 Solvable and nilpotent Lie algebras Etingof Ch. 15
9 Semisimplicity and reductivity Etingof Ch. 16–17
10 Classification of ss Lie algebras, I Etingof Ch. 19
11 Classification of ss Lie algebras, II Etingof Ch. 20
12 Root systems and Weyl groups Etingof Ch. 21–22
13 Weyl groups and Dynkin diagrams Etingof Ch. 22–23
14 Construction of Lie algebras from Dynkin diagrams Etingof Ch. 24
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