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My question is: How can I construct the Dynkin diagrams of a semisimple Lie algebra $L$ which is the direct sum of simple Lie algebras, such as for example $\text {su}(2)\oplus\text{su}(2)\oplus\text{su}(2)$? Is it the combination of Dynkin diagrams of the simple Lie algebras?

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migrated from Oct 6 '13 at 23:46

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Would Mathematics be a better home for this question? – Qmechanic Oct 6 '13 at 18:34

From what I understand, for semisimple Lie algebra you draw disconnected Dynkin diagram. So for your example it would be three disconnected vertices (since the corresponding root system is $A_1\times A_1\times A_1$).

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