Levi decomposition

In Lie theory and representation theory, the Levi decomposition, conjectured by Killing and Cartan and proved by Eugenio EliaLevi (1905), states that any finite-dimensional real Lie algebra g 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. The Levi decomposition implies that any finite-dimensional Lie algebra is a semidirect product of a solvable Lie algebra and a semisimple Lie algebra.

单词	Levi decomposition
释义	Levi decomposition 英语百科 Levi decomposition In Lie theory and representation theory, the Levi decomposition, conjectured by Killing and Cartan and proved by Eugenio EliaLevi (1905), states that any finite-dimensional real Lie algebra g 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. The Levi decomposition implies that any finite-dimensional Lie algebra is a semidirect product of a solvable Lie algebra and a semisimple Lie algebra.
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