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> Is there a real semisimple Lie group whose center is infinite?
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The **center** of a Lie group $G$ is the subgroup
$$Z\_G:=\{g\in G:gh=hg,\forall h\in G\}.$$

If $G$ is semisimple, $\mathrm{Lie}(Z\_G)=Z\_{\mathfrak{g}}=0$, so $Z\_G$ is discrete. But is it possible that $Z\_G=\mathbb{Z}$ for example?