Theorems · Theorem · nonassociative algebras
LieSubalgebra.ideal_in_normalizer
∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
{H : LieSubalgebra R L} {x y : L}, x ∈ H.normalizer → y ∈ H → ⁅x, y⁆ ∈ HA Lie subalgebra is an ideal of its normalizer.
- Defined in
- Mathlib.Algebra.Lie.Normalizer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketstatement · cited by 642
- LieSubalgebrastatement and proof · cited by 418
- neg_mem_iffproof · cited by 42
- lie_skewproof · cited by 26
- LieSubalgebra.normalizerstatement and proof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- LieSubalgebra.exists_nested_lieIdeal_ofLe_normalizerproof · cited by 1