Lie groups Notes

• Historical review
• Informal look
• Concept of a manifold
• Concept of a Lie group
• Matrix exponentials
• Matrix Lie groups
• BCH formula
• Lie algebra and the exponential map
• Lie group - Lie algebra correspondence.
• Subgroups and homogenious spaces.
• Representation of compact Lie groups.
• Hilbert's fifth problem for compact groups:  Von Neumann's theorem.