Theorems · Theorem · group theory
spinGroup.units_involute_act_eq_conjAct
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{Q : QuadraticForm R M} {x : (CliffordAlgebra Q)ˣ},
↑x ∈ spinGroup Q →
∀ (y : M),
CliffordAlgebra.involute ↑x * (CliffordAlgebra.ι Q) y * ↑x⁻¹ = ConjAct.toConjAct x • (CliffordAlgebra.ι Q) y- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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- DFunLike.coestatement and proof · cited by 62,936
- 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
- AlgHomstatement · cited by 3,236
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- MulEquivstatement · cited by 1,142
- QuadraticFormstatement and proof · cited by 507
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