Theorems · Theorem · nonassociative algebras
LieAlgebra.isLieAbelian_iff_center_eq_top
∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L], IsLieAbelian L ↔ LieAlgebra.center R L = ⊤
- Defined in
- Mathlib.Algebra.Lie.Abelian
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- 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
- Top.topstatement · cited by 9,680
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealstatement · cited by 282
- IsLieAbelianstatement · cited by 55
- LieAlgebra.centerstatement · cited by 23
- LieModule.isTrivial_iff_max_triv_eq_topproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.isLieAbelian_iff_subsingletonproof · cited by 1
- LieAlgebra.subsingleton_of_hasTrivialRadical_lie_abelianproof · cited by 0