# Simply connected semisimple algebraic group is a direct product of simply connected simple groups

In general, a semisimple algebraic group is an almost-direct product of almost-simple groups. However for simply connected semisimple algebraic groups, it holds that they are a direct product of simply connected simple algebraic groups.

I tried to find a proof for this, but unfortunately on the internet everybody just states this fact without proof! Does someone maybe have a reference for this?

Kind regards

• For a proof, see Proposition $1.4.10$ here. – Dietrich Burde Sep 2 '16 at 19:53
• the tag abstract-algebra should be replaced with algebraic-groups – YCor Sep 4 '16 at 8:14