Theorems · Theorem · nonassociative algebras

LieAlgebra.LoopAlgebra.residuePairing_apply_apply

∀ (R : Type u_1) (A : Type u_2) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup A] [inst_4 : DistribSMul A R] [inst_5 : SMulCommClass A R R] (Φ : LinearMap.BilinForm R L)
  (f g : LieAlgebra.loopAlgebra R A L),
  ((LieAlgebra.LoopAlgebra.residuePairing R A L Φ) f) g =
    ((LieAlgebra.LoopAlgebra.toFinsupp R A L) g).sum fun a v =>
      a • (Φ (((LieAlgebra.LoopAlgebra.toFinsupp R A L) f) (-a))) v

Defined in

Mathlib.Algebra.Lie.Loop

Cited by

0 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupDistribSMulSMulCommClass