Theorems · Definition · group theory

Matrix.ProjGenLinGroup.mulActionOfGL

{n : Type u_1} →
  {R : Type u_2} →
    [inst : Fintype n] →
      [inst_1 : DecidableEq n] →
        [inst_2 : CommRing R] →
          {α : Type u_4} →
            [inst_3 : MulAction (GL n R) α] →
              (∀ (u : Rˣ) (a : α), (Matrix.GeneralLinearGroup.scalar n) u • a = a) →
                MulAction (Matrix.ProjGenLinGroup n R) α

Given an action of GL n R such that the scalar matrices act trivially, define an action of PGL n R.

Defined in

Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Projective

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommRingMulAction