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First, here's a rough outline of how the classification works:

  1. Prove that if G and H are simply connected and have the same Lie algebra, then G and H are isomorphic as Lie groups.

  2. Prove that if G is any Lie group, it's its universal cover $\tilde{G}$ inherits a natural Lie group structure for which G = $\tilde{G}/Z$ where $Z\subseteq Z(\tilde{G})$.

This reduces classification to a) understanding the Lie algebras and b) understanding the centers of simply connected Lie groups.

3. Classify (simple) Lie algebras. This is done via root diagrams (Dynkin diagrams).

4. For each simply connected compact Lie group, compute it's its center.

For references, I'd check out Fulton and Harris' book "Representation Theory". I'm not sure if it actually does 4., but that's a fairly easy excercise exercise afterwards (except for perhaps the exceptional groups).
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First, here's a rough outline of how the classification works:

  1. Prove that if G and H are simply connected and have the same Lie algebra, then G and H are isomorphic as Lie groups.

  2. Prove that if G is any Lie group, it's universal cover $\tilde{G}$ inherits a natural Lie group structure for which G = $\tilde{G}/Z$ where $Z\subseteq Z(\tilde{G})$.

This reduces classification to a) understanding the Lie algebras and b) understanding the centers of simply connected Lie groups.

3. Classify (simple) Lie algebras. This is done via root diagrams (Dynkin diagrams).

4. For each simply connected compact Lie group, compute it's center.

For references, I'd check out Fulton and Harris' book "Representation Theory". I'm not sure if it actually does 4., but that's a fairly easy excercise afterwards (except for perhaps the exceptional groups).
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First, here's a rough outline of how the classification works:

  1. Prove that if G and H are simply connected and have the same Lie algebra, then G and H are isomorphic as Lie groups.

  2. Prove that if G is any Lie group, it's universal cover $\tilde{G}$ inherits a natural Lie group structure for which G = $\tilde{G}/Z$ where $Z\subseteq Z(\tilde{G})$.

This reduces classification to a) understanding the Lie algebras and b) understanding the centers of simply connected Lie groups.

3. Classify (simple) Lie algebras. This is done via root diagrams (Dynkin diagrams).

4. For each simply connected compact Lie group, compute it's center.

For references, I'd check out Fulton and Harris book "Representation Theory". I'm not sure if it actually does 4., but that's a fairly easy excercise afterwards (except for perhaps the exceptional groups).
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