What means the following expression:
Every action of an affine algebraic group on an affine algebraic variety can be linearized.
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Diego Silvera
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Where is that sentence from? – Tobias Kildetoft Jan 09 '13 at 20:12
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I have a problem which say: "Accepting that every action of an affine algebraic group on an affine algebraic variety can be linearized prove that every affine algebraic group is isomorphic ta a closed subgroup of $GL_n$, for some $n$." – Diego Silvera Jan 09 '13 at 20:17
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That does not actually say where it is from. – Tobias Kildetoft Jan 09 '13 at 20:19
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It's only an exercise that I have to do, I don't know where it's from. – Diego Silvera Jan 09 '13 at 20:22
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Then it might be better to ask whoever gave you the exercise. – Tobias Kildetoft Jan 09 '13 at 20:23
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This statement should mean the following:
There exists a finite-dimensional vector space $V$ on which the affine algebraic group $G$ acts in such a way that the affine algebraic variety $X$ is a subvariety of $V$ and the action of $G$ on $V$ restricts to the given action of $G$ on $X$.
Michael Joyce
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