Theorems · Theorem · nonassociative algebras
LieSubalgebra.normalizer_eq_self_of_isCartanSubalgebra
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (H : LieSubalgebra R L)
[H.IsCartanSubalgebra], H.toLieSubmodule.normalizer = H.toLieSubmodule- Defined in
- Mathlib.Algebra.Lie.CartanSubalgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Submoduleproof · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieSubmodulestatement · cited by 489
- LieSubalgebrastatement and proof · cited by 418
- LieSubmodule.toSubmoduleproof · cited by 150
- LieSubalgebra.IsCartanSubalgebrastatement and proof · cited by 135
- LieSubalgebra.toSubmoduleproof · cited by 90
- LieSubmodule.toSubmodule_injproof · cited by 34
- LieSubalgebra.toLieSubmodulestatement and proof · cited by 26
- LieSubmodule.normalizerstatement and proof · cited by 21
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.zeroRootSubalgebra_eq_of_is_cartanproof · cited by 2
- LieSubalgebra.ucs_eq_self_of_isCartanSubalgebraproof · cited by 1
- LieSubalgebra.isCartanSubalgebra_iff_isUcsLimitproof · cited by 0