Theorems · Theorem · linear algebra

CliffordAlgebra.ofProd_comp_toProd

∀ {R : Type u_1} {M₁ : Type u_2} {M₂ : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M₁]
  [inst_2 : AddCommGroup M₂] [inst_3 : Module R M₁] [inst_4 : Module R M₂] (Q₁ : QuadraticForm R M₁)
  (Q₂ : QuadraticForm R M₂),
  (CliffordAlgebra.ofProd Q₁ Q₂).comp (CliffordAlgebra.toProd Q₁ Q₂) =
    AlgHom.id R (GradedTensorProduct R (CliffordAlgebra.evenOdd Q₁) (CliffordAlgebra.evenOdd Q₂))

Defined in

Mathlib.LinearAlgebra.CliffordAlgebra.Prod

Cited by

0 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModule