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My question is how to construct the Dynkin diagrams of a semi-simple Lie group $G$, which is the product of simple Lie groups. Is it the combinaison of Dynkin diagrams of these simple Lie groups? For example, what would the Dynkin diagram of $SU(2)\times SU(2)\times SU(2)$ look like?

HSN
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user30656
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    it's just the disjoint union of Dynkin diagrams of the simple Lie groups. In your example it's 3 points and no edge. – user8268 Oct 06 '13 at 19:29

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