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).
Famous quotes containing the word criterion:
“I divide all literary works into two categories: Those I like and those I dont like. No other criterion exists for me.”
—Anton Pavlovich Chekhov (18601904)