Theorems · Theorem · nonassociative algebras
LieDerivation.ad_ker_eq_center
∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L], (LieDerivation.ad R L).ker = LieAlgebra.center R L
The kernel of the adjoint action on a Lie algebra is equal to its center.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketproof · cited by 642
- LieIdealstatement and proof · cited by 282
- LieDerivationstatement · cited by 95
- LieHom.kerstatement and proof · cited by 37
- LieAlgebra.centerstatement and proof · cited by 23
- LieSubmodule.extproof · cited by 20
- LieDerivation.adstatement and proof · cited by 19
- LieHom.mem_kerproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- LieDerivation.maxTrivSubmodule_eq_bot_of_center_eq_botproof · cited by 0
- LieDerivation.injective_ad_of_center_eq_botproof · cited by 0
- LieDerivation.IsKilling.ad_apply_eq_zero_iffproof · cited by 0