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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 '11 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 '11 at 20:19
    
İt is too late to edit. But you are right, my question is –  gauss Jun 28 '11 at 7:58
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closed as not a real question by Mariano Suárez-Alvarez, Igor Rivin, Simon Thomas, Martin Brandenburg, Qiaochu Yuan Jun 27 '11 at 22:49

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

1 Answer

up vote 7 down vote accepted

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 '11 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 '11 at 12:50
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