Theorems · Theorem · nonassociative algebras

DirectSum.bracket_apply_apply

∀ {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]
  (x y : DirectSum ι fun i => ↥(ℒ i)),
  ⁅x, y⁆ =
    (DirectSum.decomposeLinearEquiv ℒ)
      ⁅(DirectSum.decomposeLinearEquiv ℒ).symm x, (DirectSum.decomposeLinearEquiv ℒ).symm y⁆

Defined in

Mathlib.Algebra.Lie.Graded

Cited by

0 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidCommRingLieRingLieAlgebraGradedLieAlgebra