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  In the mathematical field of Lie theory, the radical of a Lie algebra is the largest solvable ideal of A similar notion is a Borel subalgebra, which is a (not necessarily unique) maximal solvable subalgebra.
 In the mathematical field of Lie theory, the radical of a Lie algebra is the largest solvable ideal of The radical, denoted by , fits into the exact sequence . where is semisimple. When the ground field has characteristic zero and has finite dimension, then 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 quotient map A similar notion is a Borel subalgebra, which is a (not necessarily unique) maximal solvable subalgebra.
 In the mathematical field of Lie theory, the radical of a Lie algebra is the largest solvable ideal of 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.

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  In the mathematical field of Lie theory, the radical of a Lie algebra is the largest solvable ideal of A similar notion is a Borel subalgebra, which is a (not necessarily unique) maximal solvable subalgebra.
 In the mathematical field of Lie theory, the radical of a Lie algebra is the largest solvable ideal of The radical, denoted by , fits into the exact sequence . where is semisimple. When the ground field has characteristic zero and has finite dimension, then 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 quotient map A similar notion is a Borel subalgebra, which is a (not necessarily unique) maximal solvable subalgebra.
 In the mathematical field of Lie theory, the radical of a Lie algebra is the largest solvable ideal of 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.

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