Theorems · Definition · group theory

Matrix.ProjectiveSpecialLinearGroup.toPGL

{n : Type u_1} →
  {R : Type u_2} →
    [inst : Fintype n] →
      [inst_1 : DecidableEq n] →
        [inst_2 : CommRing R] → Matrix.ProjectiveSpecialLinearGroup n R →* Matrix.ProjGenLinGroup n R

The natural inclusion map from PSL(n, R) to PGL(n, R) induced by the inclusion map from SL(n, R) to GL(n, R).

Defined in: Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Projective
Cited by: 4 results in Mathlib
Foundations: Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype DecidableEq CommRing

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Around this declaration

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.

CommRingstatement and proof · cited by 17,173
Fintypestatement and proof · cited by 7,736
MonoidHomstatement · cited by 3,629
Matrix.SpecialLinearGroupstatement and proof · cited by 348
Subgroup.centerstatement and proof · cited by 121
Matrix.ProjGenLinGroupstatement · cited by 23
Matrix.ProjectiveSpecialLinearGroupstatement · cited by 9
QuotientGroup.liftproof · cited by 8
Matrix.SpecialLinearGroup.toPGLproof · cited by 2

Cited by6

Results whose statement or proof uses this declaration.

Matrix.ProjectiveSpecialLinearGroup.toPGL_surj_of_rootsstatement · cited by 1
Matrix.ProjectiveSpecialLinearGroup.toPGL_injectivestatement · cited by 0
Matrix.ProjectiveSpecialLinearGroup.toPGL_mkstatement · cited by 0
Matrix.ProjectiveSpecialLinearGroup.toPGL_surj_iffstatement and proof · cited by 0
Matrix.ProjectiveSpecialLinearGroup.isoPSLOfAlgClosedproof · cited by 0
Matrix.ProjectiveSpecialLinearGroup.isoPSLOfAlgClosedOfNonemptyproof · cited by 0