Elementary properties of Lie groups and Lie algebras: topological properties, exponential map, lifting of Lie algebra homomorphisms. Compact Lie groups: maximal tori, Weyl group, simply connected compact Lie groups. Root systems. Irreducible representations: weights and characters. Peter-Weyl theorem. Borel-Weil theorem. Three term hours; lectures. (3.0 credit units)
Elementary properties of Lie groups and Lie algebras: topological properties, exponential map, lifting of Lie algebra homomorphisms. Compact Lie groups: maximal tori, Weyl group, simply connected compact Lie groups. Root systems. Irreducible representations: weights and characters. Peter-Weyl theorem. Borel-Weil theorem. Three term hours; lectures. (3.0 credit units)
