# 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 -0600
**

Seen: **130 times**

Last updated: **Aug 16 '13**

generalized Gell-Mann matrices

R-module/algebra valued differential forms

Monomial coefficients in a PBW basis

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

Dimensions of modules in branching

Differential forms and tensors

Coercion from PBW to universal enveloping algebra

Scaling and tensor product for Lie Groups

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 $B(X,Y) = \textrm{Trace}(XY)$ .