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
Canonical name	LiesTheorem
Date of creation	2013-03-22 13:20:40
Last modified on	2013-03-22 13:20:40
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	6
Author	bwebste (988)
Entry type	Theorem
Classification	msc 17B30