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Mathematics
Linear and Abstract Algebra
What is the definition of a Semi-simple Lie algebra?
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[QUOTE="Silviu, post: 5956546, member: 588158"] Hello! I am a bit confused by some definitions. We have that a Lie algebra is abelian if ##[a,b]=0## for all ##a,b \in L## and ##L'## is an invariant subalgebra of ##L## if ##[a,b]=0## for all ##a \in L'## and ##b \in L##. From here I understand that ##L'## is abelian. Then they define a Semi-simple Lie algebra as an algebra which is not abelian and has no Abelian invariant Lie subalgebra. I am not sure I understand this definition. What do they mean by "no Abelian invariant Lie subalgebra". Aren't all invariant subalgebras abelian? This would mean it has no invariant subalgebra at all, but this would be the definition of Simple Lie algebra. What am I missing here? [/QUOTE]
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What is the definition of a Semi-simple Lie algebra?
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