Theorems · Theorem · nonassociative algebras
LieAlgebra.center_eq_bot
∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [LieModule.IsFaithful R L L], LieAlgebra.center R L = ⊥
- Defined in
- Mathlib.Algebra.Lie.Abelian
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Quot.sound
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
- Bot.botstatement · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealstatement · cited by 282
- LieAlgebra.centerstatement · cited by 23
- LieModule.IsFaithfulstatement and proof · cited by 13
- LieAlgebra.isFaithful_self_iffproof · cited by 1
Cited by3
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
- LieDerivation.IsKilling.ad_apply_eq_zero_iffproof · cited by 0