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 Élie Cartan (1894).
Read more about Cartan's Criterion: Cartan's Criterion For Solvability, Cartan's Criterion For Semisimplicity, Examples
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“Faith in reason as a prime motor is no longer the criterion of the sound mind, any more than faith in the Bible is the criterion of righteous intention.”
—George Bernard Shaw (1856–1950)