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Theorems · Theorem · nonassociative algebras

LieDerivation.ad_apply_lieDerivation

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (x : L)
  (D : LieDerivation R L L), (LieDerivation.ad R L) (D x) = -⁅x, D⁆
Defined in
Mathlib.Algebra.Lie.AdjointAction.Derivation
Cited by
1 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingLieRingLieAlgebra
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LieDerivation.lie_der_ad_eq_ad_der · cited by 1LieDerivation.lie_der_ad_…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraBracket.bracket · cited by 642Bracket.bracketLieHom · cited by 382LieHomLieDerivation · cited by 95LieDerivationLieDerivation.ad · cited by 19LieDerivation.adLieDerivation.ad_apply_lieDer…CITED BYCITES

Cites8

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