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Theorems · Theorem · nonassociative algebras

LieAlgebra.isFaithful_self_iff

∀ (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
1 results in Mathlib
Foundations
Depth 54 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.

LieAlgebra.center_eq_bot · cited by 3LieAlgebra.center_eq_botCommRing · cited by 17173CommRingBot.bot · cited by 4720Bot.botLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieIdeal · cited by 282LieIdealLieAlgebra.center · cited by 23LieAlgebra.centerLieModule.IsFaithful · cited by 13LieModule.IsFaithfulLieAlgebra.self_module_ker_eq_center · cited by 3LieAlgebra.self_module_ke…LieModule.isFaithful_iff_ker_eq_bot · cited by 2LieModule.isFaithful_iff_…LieAlgebra.isFaithful_self_iffCITED BYCITES

Cites9

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Cited by1

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