Theorems · Theorem · nonassociative algebras

LieDerivation.ofGradingSum_of

∀ {ι : Type u_1} {R : Type u_3} {L : Type u_4} [inst : DecidableEq ι] [inst_1 : AddCommMonoid ι] [inst_2 : CommRing R]
  [inst_3 : LieRing L] [inst_4 : LieAlgebra R L] (ℒ : ι → Submodule R L) [inst_5 : GradedLieAlgebra ℒ] (φ : ι →+ R)
  (i : ι) (a : ↥(ℒ i)),
  (LieDerivation.ofGradingSum ℒ φ) ((DirectSum.of (fun x => ↥(ℒ x)) i) a) = φ i • (DirectSum.of (fun x => ↥(ℒ x)) i) a

Defined in

Mathlib.Algebra.Lie.Graded

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidCommRingLieRingLieAlgebraGradedLieAlgebra