Theorems · Definition · nonassociative algebras

DirectSum.decomposeLieEquiv

{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] → L ≃ₗ⁅R⁆ DirectSum ι fun i => ↥(ℒ i)

If L is graded by ι with degree i component ℒ i, then it is isomorphic as a Lie algebra to a direct sum of components.

Defined in

Mathlib.Algebra.Lie.Graded

Cited by

0 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidCommRingLieRingLieAlgebraGradedLieAlgebra