Rebuild a linear algebraic group from its orbits The Next CEO of Stack OverflowWhy the projection map to the semisimple part is a morphism for algebraic groups?Rigidity of Diagonalizable Algebraic GroupsProjective Special Linear Group is an Linear Algebraic GroupIdentifying the cotangent bundle of the flag varietyBoundary is a union of orbits with strictly lower dimensionIf $phi: X rightarrow Y$ is a morphism of varieties, then $phi(X)$ contains a nonempty open subset of $overlinephi(X)$.Why the chevalley $G/B$ and plucker $G/B$ are isomorphic $G$- projective varietiesComplex reductive Lie group is algebraicDoes this categorical quotient exist?Definition of simple linear algebraic group
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Rebuild a linear algebraic group from its orbits
The Next CEO of Stack OverflowWhy the projection map to the semisimple part is a morphism for algebraic groups?Rigidity of Diagonalizable Algebraic GroupsProjective Special Linear Group is an Linear Algebraic GroupIdentifying the cotangent bundle of the flag varietyBoundary is a union of orbits with strictly lower dimensionIf $phi: X rightarrow Y$ is a morphism of varieties, then $phi(X)$ contains a nonempty open subset of $overlinephi(X)$.Why the chevalley $G/B$ and plucker $G/B$ are isomorphic $G$- projective varietiesComplex reductive Lie group is algebraicDoes this categorical quotient exist?Definition of simple linear algebraic group
$begingroup$
I have the following situation (following the proof that every linear compact group is algebraic from Vinberg, Gorbatsevich and Onishchik "Lie Groups and Lie algebras III" Chapter 4 Theorem 2.1):
Let $rho : G rightarrow GL(V)$ be a faithful linear representation (say over the reals or complex) of $G$ such that the orbits $Gcdot v$ for $vin V$ are algebraic varieties in $V$. Then $G$ is an algebraic subgroup of $GL(V)$.
I cannot get how to rebuild algebraic information from the orbits. If I have a morphism of $V$ I can tell for each element of a basis if its image is in its orbit but I could have all diferent elements of $G$ acting in each basis vector...
algebraic-groups linear-groups
asked Mar 19 at 20:45
WrabbitWWrabbitW
1649
$endgroup$
add a comment |
$begingroup$
I have the following situation (following the proof that every linear compact group is algebraic from Vinberg, Gorbatsevich and Onishchik "Lie Groups and Lie algebras III" Chapter 4 Theorem 2.1):
Let $rho : G rightarrow GL(V)$ be a faithful linear representation (say over the reals or complex) of $G$ such that the orbits $Gcdot v$ for $vin V$ are algebraic varieties in $V$. Then $G$ is an algebraic subgroup of $GL(V)$.
I cannot get how to rebuild algebraic information from the orbits. If I have a morphism of $V$ I can tell for each element of a basis if its image is in its orbit but I could have all diferent elements of $G$ acting in each basis vector...
algebraic-groups linear-groups
asked Mar 19 at 20:45
WrabbitWWrabbitW
1649
$endgroup$
add a comment |
$begingroup$
I have the following situation (following the proof that every linear compact group is algebraic from Vinberg, Gorbatsevich and Onishchik "Lie Groups and Lie algebras III" Chapter 4 Theorem 2.1):
Let $rho : G rightarrow GL(V)$ be a faithful linear representation (say over the reals or complex) of $G$ such that the orbits $Gcdot v$ for $vin V$ are algebraic varieties in $V$. Then $G$ is an algebraic subgroup of $GL(V)$.
I cannot get how to rebuild algebraic information from the orbits. If I have a morphism of $V$ I can tell for each element of a basis if its image is in its orbit but I could have all diferent elements of $G$ acting in each basis vector...
algebraic-groups linear-groups
asked Mar 19 at 20:45
WrabbitWWrabbitW
1649
$endgroup$
I have the following situation (following the proof that every linear compact group is algebraic from Vinberg, Gorbatsevich and Onishchik "Lie Groups and Lie algebras III" Chapter 4 Theorem 2.1):
Let $rho : G rightarrow GL(V)$ be a faithful linear representation (say over the reals or complex) of $G$ such that the orbits $Gcdot v$ for $vin V$ are algebraic varieties in $V$. Then $G$ is an algebraic subgroup of $GL(V)$.
I cannot get how to rebuild algebraic information from the orbits. If I have a morphism of $V$ I can tell for each element of a basis if its image is in its orbit but I could have all diferent elements of $G$ acting in each basis vector...
algebraic-groups linear-groups
algebraic-groups linear-groups
asked Mar 19 at 20:45
WrabbitWWrabbitW
1649
asked Mar 19 at 20:45
WrabbitWWrabbitW
1649
asked Mar 19 at 20:45
WrabbitWWrabbitW
1649
asked Mar 19 at 20:45
WrabbitWWrabbitW
1649
asked Mar 19 at 20:45
WrabbitWWrabbitW
1649
1649
add a comment |
add a comment |
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active
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