In Lie theory and representation theory, the Levi decomposition, conjectured by Wilhelm Killing and Élie Cartan and proved by Eugenio Elia Levi (1905), states that any finite-dimensional Lie algebra g over a field of characteristic zero is the semidirect product of a solvable ideal and a semisimple subalgebra. One is its radical, a maximal solvable ideal, and the other is a semisimple subalgebra, called a Levi subalgebra.
In Lie theory and representation theory, the Levi decomposition, conjectured by Wilhelm Killing and Élie Cartan and proved by Eugenio Elia Levi (1905), states that any finite-dimensional Lie algebra g over a field of characteristic zero is the semidirect product of a solvable ideal and a semisimple subalgebra. One is its radical, a maximal solvable ideal, and the other is a semisimple subalgebra, called a Levi subalgebra.
Source: Wikipedia "Levi decomposition" · CC BY-SA 4.0
Share this article: X · Bluesky