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let G be an algebraic group. which subgroups of G are codimension one subgroups.

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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. – Mariano Suárez-Alvarez Jun 27 2011 at 19:53
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 @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. – André Henriques Jun 27 2011 at 20:19
İt is too late to edit. But you are right, my question is – gauss Jun 28 2011 at 7:58

closed as not a real question by Mariano Suárez-Alvarez, Igor Rivin, Simon Thomas, Martin Brandenburg, Qiaochu Yuan Jun 27 2011 at 22:49

1 Answer

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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.

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 thanks for your answer jvp. This is the answer of my question. – gauss Jun 28 2011 at 7:10
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 You are welcome. Could you please edit your original question following the guidelines mentioned in the comments ? It will help to make this a better site. Thanks. – jvp Jun 28 2011 at 12:50

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