Cartan's Criterion

In mathematics, Cartan's criterion gives conditions for a Lie algebra in characteristic 0 to be solvable, which implies a related criterion for the Lie algebra to be semisimple. It is based on the notion of the Killing form, a symmetric bilinear form on defined by the formula

where tr denotes the trace of a linear operator. The criterion was introduced by √Člie Cartan (1894).

Read more about Cartan's Criterion:  Cartan's Criterion For Solvability, Cartan's Criterion For Semisimplicity, Examples

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