Group Actions
Let G be a unipotent group acting on an affine variety. Then every G-orbit in the variety is closed.
The Borel fixed-point theorem states that a connected solvable group acting on a non-empty complete variety admits a fixed point. The classical Lie–Kolchin theorem follows from the theorem applied to the flag variety.
Read more about this topic: Linear Algebraic Group
Famous quotes containing the words group and/or actions:
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—Vladimir Nabokov (1899–1977)
“Words are also actions, and actions are a kind of words.”
—Ralph Waldo Emerson (1803–1882)