# 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: **131 times**

Last updated: **Aug 16 '13**

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