Properties of Lie algebras

Toral subalgebra

In mathematics, a toral subalgebra is a Lie subalgebra of a general linear Lie algebra all of whose elements are semisimple (or diagonalizable over an algebraically closed field). Equivalently, a Lie algebra is toral if it contains no nonzero nilpotent elements. Over an algebraically closed field, every toral Lie algebra is abelian; thus, its elements are simultaneously diagonalizable. (Wikipedia).

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Related pages

Abelian Lie algebra | Nilpotent Lie algebra | Semisimple Lie algebra | Nilpotent | Engel's theorem | Reductive Lie algebra | Mathematics | Diagonalizable matrix | Maximal torus | Semisimple operator | Cartan subalgebra | Killing form