Elementary question in reductive group
1
$begingroup$
I am very sorry for asking some elementary question.
Let $G$ be a reductive group over a number field $F$ and $N$ a unipotent radical of some parabolic subgroup of $G$.
Then I am wondering whether $G times N$ is a reductive group?
I will appreciate if you give me an answer in this.
Thank you in advance
algebraic-groups reductive-groups
asked Dec 17 '18 at 18:10
user29422user29422
42637
$endgroup$
add a comment |
1
$begingroup$
I am very sorry for asking some elementary question.
Let $G$ be a reductive group over a number field $F$ and $N$ a unipotent radical of some parabolic subgroup of $G$.
Then I am wondering whether $G times N$ is a reductive group?
I will appreciate if you give me an answer in this.
Thank you in advance
algebraic-groups reductive-groups
asked Dec 17 '18 at 18:10
user29422user29422
42637
$endgroup$
$begingroup$
Asking an elementary question is not a problem on this site. Asking any question, with no context is THE problem here. I shouldn't have to tutor you wrt how to ask a good question, given your rep; but please see How to ask a good question.
$endgroup$
– amWhy
Dec 17 '18 at 18:15
$begingroup$
The radical of an algebraic group is the largest normal closed, connected,solvable subgroup. A group is reductive if the radical has no unipotent elements. If $R(G)$ is the radical of $G$, what can you say about the radical of $G times N$?
$endgroup$
– D_S
Dec 17 '18 at 18:18
2
$begingroup$
Cross-posted: mathoverflow.net/questions/318873
$endgroup$
– Watson
Dec 17 '18 at 18:31
1
$begingroup$
Please do not crosspost.
$endgroup$
– Dietrich Burde
Dec 17 '18 at 20:01
add a comment |
1
1
1
$begingroup$
I am very sorry for asking some elementary question.
Let $G$ be a reductive group over a number field $F$ and $N$ a unipotent radical of some parabolic subgroup of $G$.
Then I am wondering whether $G times N$ is a reductive group?
I will appreciate if you give me an answer in this.
Thank you in advance
algebraic-groups reductive-groups
asked Dec 17 '18 at 18:10
user29422user29422
42637
$endgroup$
I am very sorry for asking some elementary question.
Let $G$ be a reductive group over a number field $F$ and $N$ a unipotent radical of some parabolic subgroup of $G$.
Then I am wondering whether $G times N$ is a reductive group?
I will appreciate if you give me an answer in this.
Thank you in advance
algebraic-groups reductive-groups
algebraic-groups reductive-groups
asked Dec 17 '18 at 18:10
user29422user29422
42637
asked Dec 17 '18 at 18:10
user29422user29422
42637
asked Dec 17 '18 at 18:10
user29422user29422
42637
asked Dec 17 '18 at 18:10
user29422user29422
42637
asked Dec 17 '18 at 18:10
user29422user29422
42637
42637
$begingroup$
Asking an elementary question is not a problem on this site. Asking any question, with no context is THE problem here. I shouldn't have to tutor you wrt how to ask a good question, given your rep; but please see How to ask a good question.
$endgroup$
– amWhy
Dec 17 '18 at 18:15
$begingroup$
The radical of an algebraic group is the largest normal closed, connected,solvable subgroup. A group is reductive if the radical has no unipotent elements. If $R(G)$ is the radical of $G$, what can you say about the radical of $G times N$?
$endgroup$
– D_S
Dec 17 '18 at 18:18
2
$begingroup$
Cross-posted: mathoverflow.net/questions/318873
$endgroup$
– Watson
Dec 17 '18 at 18:31
1
$begingroup$
Please do not crosspost.
$endgroup$
– Dietrich Burde
Dec 17 '18 at 20:01
add a comment |
$begingroup$
Asking an elementary question is not a problem on this site. Asking any question, with no context is THE problem here. I shouldn't have to tutor you wrt how to ask a good question, given your rep; but please see How to ask a good question.
$endgroup$
– amWhy
Dec 17 '18 at 18:15
$begingroup$
The radical of an algebraic group is the largest normal closed, connected,solvable subgroup. A group is reductive if the radical has no unipotent elements. If $R(G)$ is the radical of $G$, what can you say about the radical of $G times N$?
$endgroup$
– D_S
Dec 17 '18 at 18:18
2
$begingroup$
Cross-posted: mathoverflow.net/questions/318873
$endgroup$
– Watson
Dec 17 '18 at 18:31
1
$begingroup$
Please do not crosspost.
$endgroup$
– Dietrich Burde
Dec 17 '18 at 20:01
$begingroup$
Asking an elementary question is not a problem on this site. Asking any question, with no context is THE problem here. I shouldn't have to tutor you wrt how to ask a good question, given your rep; but please see How to ask a good question.
$endgroup$
– amWhy
Dec 17 '18 at 18:15
$begingroup$
Asking an elementary question is not a problem on this site. Asking any question, with no context is THE problem here. I shouldn't have to tutor you wrt how to ask a good question, given your rep; but please see How to ask a good question.
$endgroup$
– amWhy
Dec 17 '18 at 18:15
$begingroup$
The radical of an algebraic group is the largest normal closed, connected,solvable subgroup. A group is reductive if the radical has no unipotent elements. If $R(G)$ is the radical of $G$, what can you say about the radical of $G times N$?
$endgroup$
– D_S
Dec 17 '18 at 18:18
$begingroup$
The radical of an algebraic group is the largest normal closed, connected,solvable subgroup. A group is reductive if the radical has no unipotent elements. If $R(G)$ is the radical of $G$, what can you say about the radical of $G times N$?
$endgroup$
– D_S
Dec 17 '18 at 18:18
2
2
$begingroup$
Cross-posted: mathoverflow.net/questions/318873
$endgroup$
– Watson
Dec 17 '18 at 18:31
$begingroup$
Cross-posted: mathoverflow.net/questions/318873
$endgroup$
– Watson
Dec 17 '18 at 18:31
1
1
$begingroup$
Please do not crosspost.
$endgroup$
– Dietrich Burde
Dec 17 '18 at 20:01
$begingroup$
Please do not crosspost.
$endgroup$
– Dietrich Burde
Dec 17 '18 at 20:01
add a comment |
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$begingroup$
Asking an elementary question is not a problem on this site. Asking any question, with no context is THE problem here. I shouldn't have to tutor you wrt how to ask a good question, given your rep; but please see How to ask a good question.
$endgroup$
– amWhy
Dec 17 '18 at 18:15
$begingroup$
The radical of an algebraic group is the largest normal closed, connected,solvable subgroup. A group is reductive if the radical has no unipotent elements. If $R(G)$ is the radical of $G$, what can you say about the radical of $G times N$?
$endgroup$
– D_S
Dec 17 '18 at 18:18
2
$begingroup$
Cross-posted: mathoverflow.net/questions/318873
$endgroup$
– Watson
Dec 17 '18 at 18:31
1
$begingroup$
Please do not crosspost.
$endgroup$
– Dietrich Burde
Dec 17 '18 at 20:01