Theorems · Theorem · nonassociative algebras
LieSubalgebra.normalizer_engel
∀ (R : Type u_1) {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (x : L),
(LieSubalgebra.engel R x).normalizer = LieSubalgebra.engel R xEngel subalgebras are self-normalizing.
See LieSubalgebra.normalizer_eq_self_of_engel_le for a proof that Lie-subalgebras
containing an Engel subalgebra are also self-normalizing,
provided that the ambient Lie algebra is Artinian.
- Defined in
- Mathlib.Algebra.Lie.EngelSubalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- le_antisymmproof · cited by 2,068
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Endproof · cited by 774
- Bracket.bracketproof · cited by 642
- LieSubalgebrastatement · cited by 418
- pow_succproof · cited by 374
- LieAlgebra.adproof · cited by 49
- neg_mem_iffproof · cited by 42
- lie_skewproof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.exists_isCartanSubalgebra_engel_of_finrank_le_cardproof · cited by 1