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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.

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Knapp's proof that the fundamental group of a compact semisimple Lie group is finite

It seems to me that you are right and that the proof does not need the detour to linear Lie groups. I think the reason why Knapp writes the proof of his Theorem 4.26 in this way is that throughout par …
Maarten Solleveld's user avatar