Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $G$ be a compact, simply connected Lie group, and $H$ is its Lie subgroup that is also compact and simply connected, and has the same dimension with $G$, then should $H=G$? Note that these imply that the Lie group $G$ and $H$ are locally isomorphic (consider a small neighborhood around the identity).

share|improve this question
What happens if $H=\left\{ 1_G \right\}$? –  busman Nov 18 '13 at 12:00
Sorry, I've modified my question just now. –  Lao-tzu Nov 18 '13 at 12:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.