The dimension of $operatornameSL(n,F)$ as a linear algebraic group
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For an algebraically closed field $F$, what is the dimension of $operatornameSL(n,F)$ as an algebraic group? Can anyone refer me to a place in the literature where this is calculated?
algebraic-geometry reference-request algebraic-groups
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up vote
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For an algebraically closed field $F$, what is the dimension of $operatornameSL(n,F)$ as an algebraic group? Can anyone refer me to a place in the literature where this is calculated?
algebraic-geometry reference-request algebraic-groups
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
For an algebraically closed field $F$, what is the dimension of $operatornameSL(n,F)$ as an algebraic group? Can anyone refer me to a place in the literature where this is calculated?
algebraic-geometry reference-request algebraic-groups
For an algebraically closed field $F$, what is the dimension of $operatornameSL(n,F)$ as an algebraic group? Can anyone refer me to a place in the literature where this is calculated?
algebraic-geometry reference-request algebraic-groups
edited Aug 26 at 10:42
Jendrik Stelzner
7,58221037
7,58221037
asked Aug 26 at 10:40
Orpheus
217111
217111
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1 Answer
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The dimension is $n^2-1$. It's a hypersurface in $F^n^2$ defined
by the equation determinant$=1$. Any text on linear algebraic groups,
for instance that by Humphreys, will have this.
Thanks for the answer. Do you know what the dimension of $Sp(2n,F)$ is?
â Orpheus
Aug 27 at 3:43
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
The dimension is $n^2-1$. It's a hypersurface in $F^n^2$ defined
by the equation determinant$=1$. Any text on linear algebraic groups,
for instance that by Humphreys, will have this.
Thanks for the answer. Do you know what the dimension of $Sp(2n,F)$ is?
â Orpheus
Aug 27 at 3:43
add a comment |Â
up vote
2
down vote
accepted
The dimension is $n^2-1$. It's a hypersurface in $F^n^2$ defined
by the equation determinant$=1$. Any text on linear algebraic groups,
for instance that by Humphreys, will have this.
Thanks for the answer. Do you know what the dimension of $Sp(2n,F)$ is?
â Orpheus
Aug 27 at 3:43
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
The dimension is $n^2-1$. It's a hypersurface in $F^n^2$ defined
by the equation determinant$=1$. Any text on linear algebraic groups,
for instance that by Humphreys, will have this.
The dimension is $n^2-1$. It's a hypersurface in $F^n^2$ defined
by the equation determinant$=1$. Any text on linear algebraic groups,
for instance that by Humphreys, will have this.
answered Aug 26 at 10:45
Lord Shark the Unknown
88.2k955115
88.2k955115
Thanks for the answer. Do you know what the dimension of $Sp(2n,F)$ is?
â Orpheus
Aug 27 at 3:43
add a comment |Â
Thanks for the answer. Do you know what the dimension of $Sp(2n,F)$ is?
â Orpheus
Aug 27 at 3:43
Thanks for the answer. Do you know what the dimension of $Sp(2n,F)$ is?
â Orpheus
Aug 27 at 3:43
Thanks for the answer. Do you know what the dimension of $Sp(2n,F)$ is?
â Orpheus
Aug 27 at 3:43
add a comment |Â
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