I would like to show that for a given affine algebraic $k$-group, where $k$ is an algebraically closed field of characteristic $0$, there is a bijective correspondence between the closed subschemes of $G$ and $\Gamma(G,\mathcal{O})$ and that it sends the algebraic subgroups of $G$ to Hopf ideals.
How could I show it? Is there any paper where I can find the proof?
Thanks.