Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Topological groups, Matrix Lie groups, examples of Matrix Lie group, the Lie algebra of a Matrix Lie group.
- The Baker-Campbell-Hausdorff formula, Correspondence of Matrix Lie group and Lie algebra homomorphisms, covering groups, subgroups and subalgebras.
- Basic Representation theory, representations of SU(2), SO(3), sl(2, C), su(2), the Heisenberg group etc., Schur lemma, complete reducibilty.
- Manifolds and Lie groups, Matrix Lie groups as Lie groups, examples of nonmatrix Lie group, Haar measure on Lie groups.
- Representation of compact Lie groups, the Peter-Weyl theorem and its applications.
- D. Bump, Lie groups, GTM 225, Springer-Verlag, New York, 2004.
- C. Chevalley, Theory of Lie Groups, Princeton Mathematical Series, vol. 8. Princeton University Press, Princeton, 1946.
- V. S. Varadarajan, Lie groups, Lie algebras, and their representations, GTM 102, Springer-Verlag, New York, 1984.
- F. Warner, Foundations of differentiable manifolds and Lie groups, GTM 94, Springer-Verlag, 1983.
