Mathlib Map

Theorems · Theorem · nonassociative algebras

LieAlgebra.self_module_ker_eq_center

∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L],
  LieModule.ker R L L = LieAlgebra.center R L
Defined in
Mathlib.Algebra.Lie.Abelian
Cited by
3 results in Mathlib
Foundations
Depth 51 from the axioms · uses propext, Quot.sound
Assumes
CommRingLieRingLieAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LieDerivation.ad_ker_eq_center · cited by 3LieDerivation.ad_ker_eq_c…LieAlgebra.isFaithful_self_iff · cited by 1LieAlgebra.isFaithful_sel…LieAlgebra.isNilpotent_range_ad_iff · cited by 0LieAlgebra.isNilpotent_ra…CommRing · cited by 17173CommRingLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraBracket.bracket · cited by 642Bracket.bracketLieIdeal · cited by 282LieIdeallie_skew · cited by 26lie_skewLieAlgebra.center · cited by 23LieAlgebra.centerLieSubmodule.ext · cited by 20LieSubmodule.extLieModule.ker · cited by 8LieModule.kerLieAlgebra.self_module_ker_eq…CITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.