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 ().
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 Élie Cartan ().
2021-04-22T05:17:40Z
2020-02-13T00:42:22Z
2020-11-10T19:09:02Z
3052668
5674
5685
2020-02-13T00:42:19Z
2020-11-10T19:08:56Z
2021-04-22T05:17:37Z
22
940517069
988048663
1019227043