Killing form

Let 𝔤 be a finite dimensional Lie algebraMathworldPlanetmath over a field k, and X,Y𝔤. Let adX:𝔤𝔤 be the adjoint action, adXY=[X,Y].

Then the Killing form on 𝔤 is a bilinear map


given by


The Killing form is invariant ( under the adjoint action and symmetricPlanetmathPlanetmath (since trace is symmetric).

Title Killing form
Canonical name KillingForm
Date of creation 2013-03-22 13:15:47
Last modified on 2013-03-22 13:15:47
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 8
Author bwebste (988)
Entry type Definition
Classification msc 17B05