# How to construct Dynkin diagrams for semisimple Lie algebras?

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?

• Would Mathematics be a better home for this question? Oct 6, 2013 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 $A_1\times A_1\times A_1$).
So then you would just draw three vertices, one for each $$A_1$$, as @Kosm explained.