Theorems · Definition · linear algebra

CliffordAlgebra.even.lift

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] →
          (Q : QuadraticForm R M) →
            {A : Type u_3} →
              [inst_3 : Ring A] →
                [inst_4 : Algebra R A] → CliffordAlgebra.EvenHom Q A ≃ (↥(CliffordAlgebra.even Q) →ₐ[R] A)

Every algebra morphism from the even subalgebra is in one-to-one correspondence with a bilinear map that sends duplicate arguments to the quadratic form, and contracts across multiplication.

Defined in

Mathlib.LinearAlgebra.CliffordAlgebra.Even

Cited by

2 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleRingAlgebra