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Max Horn
Max Horn
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Are Zariski connetedconnected and closed semisimple subgroups of semisimple and simply connected algebraic groups again simply connected algebraic groups themselves?

Let $G$ be a semisimple and simply connected linear algebraic group over $\mathbb{C}$. Let $H$ be a connected, Zariski closed and semisimple linear algebraic $\mathbb{Q}$-subgroup of $G$.

Is $H$ a simply connected linear algebraic group?

Here "simply connected" means every central isogeny to $G$ is an isomorphism.

Are Zariski conneted and closed semisimple subgroups of simply connected algebraic groups simply connected algebraic groups themselves?

Let $G$ be a semisimple simply connected linear algebraic group over $\mathbb{C}$. Let $H$ be a connected Zariski closed linear algebraic $\mathbb{Q}$-subgroup of $G$.

Is $H$ a simply connected linear algebraic group?

Here "simply connected" means every central isogeny to $G$ is an isomorphism.

Are Zariski connected and closed semisimple subgroups of semisimple and simply connected algebraic groups again simply connected?

Let $G$ be a semisimple and simply connected linear algebraic group over $\mathbb{C}$. Let $H$ be a connected, Zariski closed and semisimple linear algebraic $\mathbb{Q}$-subgroup of $G$.

Is $H$ a simply connected linear algebraic group?

Here "simply connected" means every central isogeny to $G$ is an isomorphism.

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Amir
Amir
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Are Zariski conneted and closed semisimple subgroups of simply connected algebraic groups simply connected algebraic groups themselves?

Let $G$ be a semisimple simply connected linear algebraic group over $\mathbb{C}$. Let $H$ be a connected Zariski closed linear algebraic $\mathbb{Q}$-subgroup of $G$.

Is $H$ a simply connected linear algebraic group?

Here "simply connected" means every central isogeny to $G$ is an isomorphism.