I have a very basic question on Lie algebras. I'm doing particle physics, and a lot of emphasis seems to be placed on the weight diagrams of simple Lie algebras. But these simple Lie algebras are all that ever seems to be discussed. Can anyone tell me in intuitive terms how the weight diagrams of semi-simple Lie algebras relate to those of the simple Lie algebras that sum to make the semi-simple algebras? Does one somehow 'add' the weight spaces together? (Sorry if this sounds really stoopid!)