Theorems · Theorem · nonassociative algebras

LieSubalgebra.normalizer_eq_self_of_engel_le

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [IsArtinian R L]
  (H : LieSubalgebra R L) (x : L), LieSubalgebra.engel R x ≤ H → H.normalizer = H

A Lie-subalgebra of an Artinian Lie algebra is self-normalizing if it contains an Engel subalgebra. See LieSubalgebra.normalizer_engel for a proof that Engel subalgebras are self-normalizing, avoiding the Artinian condition.

Defined in

Mathlib.Algebra.Lie.EngelSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraIsArtinian