Lie’s theorem

Let 𝔤 be a finite dimensional complex solvable Lie algebraMathworldPlanetmath, and V a repesentation of 𝔤. Then there exists an element of V which is a simultaneous eigenvectorMathworldPlanetmathPlanetmathPlanetmath for all elements of 𝔤.

Applying this result inductively, we find that there is a basis of V with respect to which all elements of 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