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課程概述 |
1.Basic Lie group theory and Lie algebra theory:
Killing form, Lie's theorem, Engel's theorem, Cartan's criterion, Semidirect product of Lie algebras(Lie groups), Fundamental theorems of Lie theory, Solvable Lie groups, Nilpotent Lie groups, Classical semisimple Lie groups.
2.Complex semisimple Lie algebras:
Cartan subalgebra, Root system, Weyl group, Cartan matrices, Serre relations, Correspondence theorem for complex semisimple Lie algebras and reduced root systems, Universal enveloping algebra.
3.Compact Lie groups and their representations:
Peter-Weyl theorem, Analytic Weyl group, Integral forms, Weyl's theorem, Theorem of the highest weight. |