Borel subgroup is conjugate-dense in connected algebraic group
Statement over an algebraically closed field
Statement over an arbitrary field
The statement as made over an algebraically closed field does not work over an arbitrary field, but we can make suitable modifications and make sure it does (can we?).
|Theorem||Value of||Value of|
|Triangulability theorem||general linear group||subgroup of upper-triangular matrices.|
|Spectral theorem for unitary matrices (not sure if this really fits)||unitary group||subgroup of unitary diagonal matrices.|