Given a Lie algebra of elements(adsbygoogle = window.adsbygoogle || []).push({}); Gsatisfying_{i}[G, it can be shown that_{i},G_{j}] = -if_{ij}^{k}G_{k}

trace(G_{i}G_{j}) = -f_{ik}^{l}f_{jl}^{k}

where by "trace" we mean the trace in a particular matrix representation.

The text in which I encountered this does not have a proof and I'm having trouble convincing myself of it. Anyone have a reference or hint that could help?

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# Lie algrebra question

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