Theorems · Definition · ring theory

CliffordAlgebra.contractLeftAux

{R : Type u1} →
  [inst : CommRing R] →
    {M : Type u2} →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] →
          (Q : QuadraticForm R M) →
            Module.Dual R M → M →ₗ[R] CliffordAlgebra Q × CliffordAlgebra Q →ₗ[R] CliffordAlgebra Q

Auxiliary construction for CliffordAlgebra.contractLeft

Defined in: Mathlib.LinearAlgebra.CliffordAlgebra.Contraction
Cited by: 5 results in Mathlib
Foundations: Depth 58 from the axioms · uses propext, Quot.sound
Assumes: CommRing AddCommGroup Module

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
LinearMap.compproof · cited by 1,642
Module.Dualstatement and proof · cited by 583
QuadraticFormstatement and proof · cited by 507
CliffordAlgebrastatement and proof · cited by 309
AlgHom.toLinearMapproof · cited by 254
CliffordAlgebra.ιproof · cited by 142
LinearMap.fstproof · cited by 64

Cited by6

Results whose statement or proof uses this declaration.

CliffordAlgebra.contractLeftproof · cited by 22
CliffordAlgebra.contractLeft_algebraMapproof · cited by 5
CliffordAlgebra.contractLeft_ι_mulproof · cited by 5
CliffordAlgebra.contractLeftAux_contractLeftAuxstatement and proof · cited by 3
CliffordAlgebra.contractLeftAux_apply_applystatement and proof · cited by 2
CliffordAlgebra.contractLeft_ιproof · cited by 2