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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!

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    $\begingroup$ What about the exercises to Humphreys book on Lie algebras? They are online with solutions. $\endgroup$ Dec 31, 2021 at 16:02
  • $\begingroup$ Will have a look! Thanks! $\endgroup$
    – Spida
    Jan 7, 2022 at 15:02

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Problems And Solutions For Groups, Lie Groups, Lie Algebras With Applications, by Steeb, Tanski & Hardy.

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