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Cartan's criterion (Theorem)

A Lie algebra $\fr g$ is semi-simple if and only if its Killing form $B_{\fr g}$ is nondegenerate.



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Cross-references: nondegenerate, Killing form, semi-simple, Lie algebra

This is version 2 of Cartan's criterion, born on 2002-12-13, modified 2002-12-16.
Object id is 3744, canonical name is CartansCriterion.
Accessed 2808 times total.

Classification:
AMS MSC: 17B20 (Nonassociative rings and algebras :: Lie algebras and Lie superalgebras :: Simple, semisimple, reductive )
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