Theorems · Theorem · group theory

Projectivization.SL_mulAction_ker

∀ {K : Type u_1} [inst : Field K] {ι : Type u_3} [inst_1 : Fintype ι] [inst_2 : DecidableEq ι],
  (MulAction.toPermHom (Matrix.SpecialLinearGroup ι K) (Projectivization K (ι → K))).ker =
    Subgroup.center (Matrix.SpecialLinearGroup ι K)

Defined in: Mathlib.LinearAlgebra.Projectivization.Action
Cited by: 1 results in Mathlib
Foundations: Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Fintype DecidableEq

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Cites43

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

DFunLike.coeproof · cited by 62,936
Moduleproof · cited by 20,661
RingHom.idproof · cited by 18,349
LinearMapproof · cited by 10,215
Fintypestatement and proof · cited by 7,736
Fieldstatement and proof · cited by 7,404
Matrixproof · cited by 4,303
Subgroupstatement · cited by 3,593
map_zeroproof · cited by 1,614
Fintype.cardproof · cited by 1,386
Equiv.Permstatement · cited by 1,375
LinearEquiv.toLinearMapproof · cited by 1,171

Cited by1

Results whose statement or proof uses this declaration.

Matrix.ProjectiveSpecialLinearGroup.toPermHom_injectiveproof · cited by 0