Theorems · Definition · linear algebra
CliffordAlgebra.even
{R : Type u_1} →
{M : Type u_2} →
[inst : CommRing R] →
[inst_1 : AddCommGroup M] → [inst_2 : Module R M] → (Q : QuadraticForm R M) → Subalgebra R (CliffordAlgebra Q)The even submodule CliffordAlgebra.evenOdd Q 0 is also a subalgebra.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Subalgebrastatement · cited by 1,353
- QuadraticFormstatement and proof · cited by 507
- CliffordAlgebrastatement · cited by 309
- CliffordAlgebra.evenOddproof · cited by 35
- Submodule.toSubalgebraproof · cited by 7
Cited by32
Results whose statement or proof uses this declaration.
- spinGroupproof · cited by 23
- CliffordAlgebra.even.ιstatement · cited by 9
- CliffordAlgebra.even.lift.auxstatement and proof · cited by 5
- CliffordAlgebra.evenToNegstatement · cited by 5
- CliffordAlgebra.toEvenstatement · cited by 4
- CliffordAlgebra.ofEvenstatement · cited by 3
- CliffordAlgebra.even.algHom_extstatement and proof · cited by 3
- CliffordAlgebra.toEven_ιstatement and proof · cited by 3
- CliffordAlgebra.even.lift.aux_applystatement and proof · cited by 2
- CliffordAlgebra.ofEven_ιstatement · cited by 2
- CliffordAlgebra.evenEquivEvenNegstatement · cited by 2
- CliffordAlgebra.even.liftstatement and proof · cited by 2