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MATH 624 Compact Lie Groups

Compact Lie groups. Classical examples. One parametric subgroups. Maximal tori. Invariant differential operators and Lie algebras. Relation between Lie groups and algebras. Killing invariant form. Universal enveloping algebra. Cartan subalgebras. Roots systems. Weyl group. Dynkin diagrams and classification of roots systems. Exceptional Lie groups and algebras. Credit units: 3 ECTS Credit units: 5.

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