Theorems · Theorem · linear algebra

CliffordAlgebra.toBaseChange_involute

∀ {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)
  (x : CliffordAlgebra (QuadraticForm.baseChange A Q)),
  (CliffordAlgebra.toBaseChange A Q) (CliffordAlgebra.involute x) =
    (TensorProduct.map LinearMap.id CliffordAlgebra.involute.toLinearMap) ((CliffordAlgebra.toBaseChange A Q) x)

The involution acts only on the right of the tensor product.

Defined in

Mathlib.LinearAlgebra.CliffordAlgebra.BaseChange

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAddCommGroupAlgebraModuleInvertible