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, #m/def/lie i.e.

Proof of Lie subalgebra

Let . Then by the Jacobi identity,

as required.

A subalgebra is the Centralizer in a Lie algebra .

Further terminology

Properties

  1. iff is a Lie algebra ideal of

See also

#state/tidy | #lang/en | #SemBr