Theorems · Definition · ring theory

CliffordAlgebra.involute

{R : Type u_1} →
  [inst : CommRing R] →
    {M : Type u_2} →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] → {Q : QuadraticForm R M} → CliffordAlgebra Q →ₐ[R] CliffordAlgebra Q

Grade involution, inverting the sign of each basis vector.

Defined in: Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation
Cited by: 36 results in Mathlib
Foundations: Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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

Cites9

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

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
AlgHomstatement · cited by 3,236
QuadraticFormstatement and proof · cited by 507
CliffordAlgebrastatement · cited by 309
CliffordAlgebra.ιproof · cited by 142
CliffordAlgebra.liftproof · cited by 13

Cited by37

Results whose statement or proof uses this declaration.

CliffordAlgebra.involute_ιstatement · cited by 12
CliffordAlgebra.involuteEquivproof · cited by 3
CliffordAlgebra.star_defstatement · cited by 3
lipschitzGroup.involute_act_ι_mem_range_ιstatement and proof · cited by 2
CliffordAlgebra.submodule_map_involute_eq_comapstatement · cited by 2
CliffordAlgebra.ι_range_map_involutestatement · cited by 2
CliffordAlgebra.involute_comp_involutestatement and proof · cited by 1
CliffordAlgebra.involute_eq_of_mem_evenstatement and proof · cited by 1
CliffordAlgebra.involute_involutivestatement · cited by 1
CliffordAlgebraComplex.toComplex_involutestatement and proof · cited by 1
spinGroup.involute_eqstatement · cited by 1
CliffordAlgebraQuaternion.toQuaternion_starproof · cited by 1