Radical_of_a_Lie_algebra
In the mathematical field of Lie theory, the radical of a Lie algebra is the largest solvable ideal of [1]
The radical, denoted by , fits into the exact sequence
- .
where is semisimple. When the ground field has characteristic zero and has finite dimension, Levi's theorem states that this exact sequence splits; i.e., there exists a (necessarily semisimple) subalgebra of that is isomorphic to the semisimple quotient via the restriction of the quotient map
A similar notion is a Borel subalgebra, which is a (not necessarily unique) maximal solvable subalgebra.