In mathematics, the Lie-Kolchin theorem is a theorem in the representation theory of linear algebraic groups.
It states that if G is a linear algebraic group,
an irreducible representation on a finite-dimensional vector space V, and B a Borel subgroup of G, then there is a one-dimensional linear subspace L of V, such that
- ρ(B)(L) = L.
That is, ρ(B) has an invariant line L, on which B therefore acts through a one-dimensional representation.
This result is named for Sophus Lie and Ellis Kolchin (1916-1991).
Applications
To be written