Theorems · Definition · group theory
Matrix.ProjGenLinGroup
(n : Type u_1) → [Fintype n] → [DecidableEq n] → (R : Type u_2) → [CommRing R] → Type (max (max u_1 u_2) u_2 u_1)
Projective general linear group $PGL(n, R)$ defined as the quotient of the general linear group by its center.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- HasQuotient.Quotientproof · cited by 2,301
- Matrix.GeneralLinearGroupproof · cited by 556
- Subgroup.centerproof · cited by 121
Cited by32
Results whose statement or proof uses this declaration.
- Matrix.ProjGenLinGroup.mkstatement · cited by 19
- Matrix.ProjectiveSpecialLinearGroup.toPGLstatement · cited by 4
- Matrix.ProjGenLinGroup.mapstatement · cited by 3
- Matrix.ProjGenLinGroup.signDetstatement · cited by 2
- Matrix.SpecialLinearGroup.toPGLstatement · cited by 2
- Matrix.ProjGenLinGroup.induction_onstatement and proof · cited by 2
- Matrix.ProjGenLinGroup.ker_mkstatement · cited by 2
- Matrix.ProjGenLinGroup.liftstatement · cited by 2
- Matrix.ProjGenLinGroup.mk_smulstatement · cited by 1
- Matrix.ProjGenLinGroup.mulActionOfGLstatement · cited by 1
- Matrix.ProjectiveSpecialLinearGroup.toPGL_surj_of_rootsstatement and proof · cited by 1
- Matrix.SpecialLinearGroup.toPGL_kerstatement · cited by 1