Lie’s theorem

Let $\mathfrak{g}$ be a finite dimensional complex solvable Lie algebra, and $V$ a repesentation of $\mathfrak{g}$. Then there exists an element of $V$ which is a simultaneous eigenvector for all elements of $\mathfrak{g}$.

Applying this result inductively, we find that there is a basis of $V$ with respect to which all elements of $\mathfrak{g}$ are upper triangular.

Title Lie’s theorem LiesTheorem 2013-03-22 13:20:40 2013-03-22 13:20:40 bwebste (988) bwebste (988) 6 bwebste (988) Theorem msc 17B30