I have an oral exam on Lie groups to prepare. During the semester we mostly had theoretical exercises to do, like proving such and such a theorem. However, the exercises during the exam are going to be more pratical, I guess like showing a group has some properties.
Through the semester, we've studied: compact groups, the Haar measure, the Lie groups and the Lie algebras, the exponential map, the adjoint representation, solvability, nilpotency, simplicity and semi-simplicity, and finally the Levi decomposition. So, I'm looking for exercises to drill these subjects.
Thank you!
Problems And Solutions For Groups, Lie Groups, Lie Algebras With Applications, by Steeb, Tanski & Hardy.