Levi’s theorem

Let 𝔀 be a complex Lie algebra, 𝔯 its radical. Then the extensionPlanetmathPlanetmathPlanetmath 0→𝔯→𝔀→𝔀/𝔯→0 is split, i.e., there exists a subalgebraPlanetmathPlanetmathPlanetmath π”₯ of 𝔀 mapping isomorphically to 𝔀/𝔯 under the natural projectionMathworldPlanetmath.

Title Levi’s theorem
Canonical name LevisTheorem
Date of creation 2013-03-22 13:51:15
Last modified on 2013-03-22 13:51:15
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Theorem
Classification msc 17B05