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Two theorems of Group Theory

  1. Aug 23, 2015 #1
    I am studying Group Theory at the moment and i am not sure about a theorem.
    Is it true that a Lie Group G is compact if and only if every finite complex representation of it is unitary?
    I know that is true the if, but what about the viceversa?
    Same question.
    Is it true that a Lie group is compact if and only if every irreducible representaion unitary is finite?
  2. jcsd
  3. Aug 28, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
  4. Aug 29, 2015 #3
    If a Lie group is not compact is it true that all its irreducibile unitary representations are infinite dimensional?
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