Lie algebras MOC

Normalizer in a Lie algebra

Let be a Lie algebra over and be a vector subspace. The normalizer of in is the Lie subalgebra of all elements whose adjoint representations leave invariant, lie i.e.

Proof of Lie subalgebra

Let . Then by the ^Jacobi,

as required.

A subalgebra is the Centralizer in a Lie algebra .

Further terminology

• A subalgebra is called self-normalizing iff .

Properties

1. iff is a Lie algebra ideal of

See also

• Normalizer in a group

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