invariant form (Lie algebras)

Let V be a representationPlanetmathPlanetmath of a Lie algebraMathworldPlanetmath 𝔤 over a field k. Then a bilinear formPlanetmathPlanetmath B:V×Vk is invariant if


for all X𝔤,v,wV. This criterion seems a little odd, but in the context of Lie algebras, it makes sense. For example, the map B~:VV* given by vB(,v) is equivariant if and only if B is an invariant form.

Title invariant form (Lie algebras)
Canonical name InvariantFormLieAlgebras
Date of creation 2013-03-22 13:15:45
Last modified on 2013-03-22 13:15:45
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Definition
Classification msc 17B15