Theorems · Definition · group theory

Projectivization.PSLAction.toPermHom

{K : Type u_1} →
  [inst : Field K] →
    {ι : Type u_3} →
      [inst_1 : Fintype ι] →
        [inst_2 : DecidableEq ι] → Matrix.ProjectiveSpecialLinearGroup ι K →* Equiv.Perm (Projectivization K (ι → K))

The action of the special linear group on ℙ F (ι → F) factors through the projective special linear group PSL = SL ⧸ Z(SL).

Defined in: Mathlib.LinearAlgebra.Projectivization.Action
Cited by: 1 results in Mathlib
Foundations: Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Fintype DecidableEq

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Cites10

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

Fintypestatement and proof · cited by 7,736
Fieldstatement and proof · cited by 7,404
MonoidHomstatement · cited by 3,629
Equiv.Permstatement · cited by 1,375
Matrix.SpecialLinearGroupstatement and proof · cited by 348
Subgroup.centerstatement and proof · cited by 121
Projectivizationstatement and proof · cited by 111
MulAction.toPermHomproof · cited by 16
Matrix.ProjectiveSpecialLinearGroupstatement · cited by 9
QuotientGroup.liftproof · cited by 8

Cited by1

Results whose statement or proof uses this declaration.

Matrix.ProjectiveSpecialLinearGroup.toPermHom_injectivestatement and proof · cited by 0