let G be an algebraic group. which subgroups of G are codimension one subgroups.
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$\begingroup$ It is not quite clear what you are asking... The dimension of a closed subgroup depends on the closed subgroup, for example! The FAQ gives some information on how best to ask questions to attract useful answers. $\endgroup$– Mariano Suárez-ÁlvarezJun 27, 2011 at 19:53
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1$\begingroup$ @bernardshow: You should edit the question (click on the "edit" button), and certainly remove the "What is the dimension of $H$?" (unless you tell us what $H$ is). Your question will probably get closed, but if you edit it and make it into a clear question, then it might et reopened. $\endgroup$– André HenriquesJun 27, 2011 at 20:19
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$\begingroup$ İt is too late to edit. But you are right, my question is $\endgroup$– gaussJun 28, 2011 at 7:58
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Perhaps it is better to phrase the question in terms of Lie algebras. For instance, if you want to know which are the possible codimension one Lie subalgebras of a given finite dimensional Lie algebra then there is a result of Tits which address exactly this.
Let $\mathfrak g$ be a finite dimensional Lie algebra over a field of characteristic zero. If $\mathfrak h$ is a codimension one subalgebra then there exists a morphism $\phi : \mathfrak g \to > \mathfrak{sl}(2)$ with kernel contained in $\mathfrak h$.
This result has been explored by Hoffman to provide a classification of codimension one subalgebras of Lie algebras in this paper.
answered Jun 27, 2011 at 20:17
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1$\begingroup$ thanks for your answer jvp. This is the answer of my question. $\endgroup$– gaussJun 28, 2011 at 7:10