What is the killing form?

Asked on 04.11.2018 in All Questions.
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Suppose we have no non-trivial solvable ideals, and as mathfrak{g} is semisimple, it is not solvable, thus the maximum solvable ideal is {0}, hence Rad(mathfrak{g})=0. 4 Rightarrow 3 Suppose we have a Lie algebra with solvable ideals, so there exists (mathfrak{i} subset mathfrak{g}) such that [mathfrak{i}supset mathfrak{i}^{(1)} supset cdots supset mathfrak{i}^{(n)}=0] then mathfrak{i}^{(n-1)} must be a one-dimensional subspace, and so must be Abelian, so Abelian Ideals imply solvability. end{proof} Now we have defined semisimplicity for...
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