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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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  • Radical de un álgebra de Lie (es)
  • 리 대수 근기 (ko)
  • Radical of a Lie algebra (en)
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  • En la teoría matemática de álgebras de Lie, el radical de un álgebra de Lie es el mayor soluble de ​ El radical, denotado como , se ajusta a la sucesión exacta donde es un álgebra de Lie semisimple. Cuando el cuerpo base tiene característica cero y tiene dimensión finita, el teorema de Levi afirma que esta sucesión exacta es divisible; es decir, existe una subálgebra (necesariamentem semisimple) de que es isomorfa al cociente semisimple a través de la restricción del mapa del cociente . Una noción similar es la de , que es una subálgebra (no necesariamente única) maximalmente soluble. (es)
  • 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. (en)
  • 리 군론에서 리 대수 근기(Lie代數根基, 영어: Lie algebra radical)는 리 대수의 최대 가해 아이디얼이다. (ko)
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  • En la teoría matemática de álgebras de Lie, el radical de un álgebra de Lie es el mayor soluble de ​ El radical, denotado como , se ajusta a la sucesión exacta donde es un álgebra de Lie semisimple. Cuando el cuerpo base tiene característica cero y tiene dimensión finita, el teorema de Levi afirma que esta sucesión exacta es divisible; es decir, existe una subálgebra (necesariamentem semisimple) de que es isomorfa al cociente semisimple a través de la restricción del mapa del cociente . Una noción similar es la de , que es una subálgebra (no necesariamente única) maximalmente soluble. (es)
  • 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. (en)
  • 리 군론에서 리 대수 근기(Lie代數根基, 영어: Lie algebra radical)는 리 대수의 최대 가해 아이디얼이다. (ko)
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