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

### Famous quotes containing the word criterion:

“I divide all literary works into two categories: Those I like and those I don’t like. No other *criterion* exists for me.”

—Anton Pavlovich Chekhov (1860–1904)