# Killing form

Hi,

is there a simple possibility to calculate the Killing form in some standard matrix Lie-Algebras like $\mathfrak{so}(n,\mathbb{R})$?

Thanks in advance for your answers!

Killing form

Hi,

is there a simple possibility to calculate the Killing form in some standard matrix Lie-Algebras like $\mathfrak{so}(n,\mathbb{R})$?

Thanks in advance for your answers!

Asked: **
2013-08-16 11:13:38 -0500
**

Seen: **126 times**

Last updated: **Aug 16 '13**

Differential forms and tensors

Dimensions of modules in branching

R-module/algebra valued differential forms

Scaling and tensor product for Lie Groups

Infinite dimensional Lie algebras in Sage

Automorphisms and derivations of Lie algebras

how to do inner product between two weights of a lie algebra?

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.

With an explicit example in mind we have a fundamental representation / setting where $n\times n$ or $(2n)\times(2n)$ matrices appear explicitly, and the Killing form can be written - up to a multiplicative constant depending on $n$ - in the form $B(X,Y) = \textrm{Trace}(XY)$ .