Theorems · Theorem · linear algebra

CliffordAlgebra.toBaseChange_comp_reverseOp

∀ {R : Type u_1} (A : Type u_2) {V : Type u_3} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : AddCommGroup V]
  [inst_3 : Algebra R A] [inst_4 : Module R V] [inst_5 : Invertible 2] (Q : QuadraticForm R V),
  (AlgHom.op (CliffordAlgebra.toBaseChange A Q)).comp CliffordAlgebra.reverseOp =
    (↑(Algebra.TensorProduct.opAlgEquiv R A A (CliffordAlgebra Q))).comp
      ((Algebra.TensorProduct.map (↑(AlgEquiv.toOpposite A A)) CliffordAlgebra.reverseOp).comp
        (CliffordAlgebra.toBaseChange A Q))

Auxiliary theorem used to prove toBaseChange_reverse without needing induction.

Defined in

Mathlib.LinearAlgebra.CliffordAlgebra.BaseChange

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAddCommGroupAlgebraModuleInvertible