Theorems · Theorem · nonassociative algebras
LieSubalgebra.mem_normalizer_iff
∀ {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 : L), x ∈ H.normalizer ↔ ∀ y ∈ H, ⁅x, y⁆ ∈ H- Defined in
- Mathlib.Algebra.Lie.Normalizer
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 642
- LieSubalgebrastatement and proof · cited by 418
- neg_mem_iffproof · cited by 42
- lie_skewproof · cited by 26
- LieSubalgebra.normalizerstatement · cited by 19
- LieSubalgebra.mem_normalizer_iff'proof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- LieSubalgebra.normalizer_engelproof · cited by 1
- LieAlgebra.zeroRootSubalgebra_normalizer_eq_selfproof · cited by 1
- LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebraproof · cited by 1
- LieSubalgebra.lie_mem_sup_of_mem_normalizerproof · cited by 1
- LieSubalgebra.normalizer_eq_self_of_engel_leproof · cited by 0