Theorems · Theorem · group theory

SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply

∀ {R : Type u_1} {V : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup V] [inst_2 : Module R V]
  [inst_3 : Module.Free R V] [inst_4 : Module.Finite R V] (g : ↥(Subgroup.center (SpecialLinearGroup R V))) (x : V),
  SpecialLinearGroup.centerEquivRootsOfUnity g • x = (fun x => ↑↑g x) x

Defined in

Mathlib.LinearAlgebra.SpecialLinearGroup

Cited by

1 results in Mathlib

Foundations

Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.FreeModule.Finite