Theorems · Definition · nonassociative algebras

LieDerivation.ofGradingSum

{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] →
                    (ι →+ R) → LieDerivation R (DirectSum ι fun i => ↥(ℒ i)) (DirectSum ι fun i => ↥(ℒ i))

A derivation on the direct sum of graded pieces of a graded Lie algebra, induced by an additive map on the grading monoid.

Defined in

Mathlib.Algebra.Lie.Graded

Cited by

2 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidCommRingLieRingLieAlgebraGradedLieAlgebra