0
$\begingroup$

Let $G$ be a connected Lie group with a compact semisimple Lie algebra. It is well known that the Lie algebra then can be written as the product of compact simple Lie algebras which are classified by Dynkin diagrams. I would like to know what we can say on the level of Lie groups, i.e. is it true that the Lie group then can be written as a product of compact simple Lie groups?

$\endgroup$
0
$\begingroup$

No, one has to take into account coverings. The smallest counterexample is $SO(4)$, which is not such a product, but whose universal cover is a product $Spin(4) \cong SU(2) \times SU(2)$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.