Theorems · Theorem · group theory

SpecialLinearGroup.centerCongr_toLin_equiv_trans_centerEquivRootsOfUnity_eq

∀ {R : Type u_4} [inst : CommRing R] {V : Type u_5} [inst_1 : AddCommGroup V] [inst_2 : Module R V]
  [inst_3 : Module.Free R V] [inst_4 : Module.Finite R V] {ι : Type u_6} [inst_5 : Fintype ι] [inst_6 : DecidableEq ι]
  (b : Module.Basis ι R V) (g : ↥(Subgroup.center (Matrix.SpecialLinearGroup ι R))),
  ↑(((Subgroup.centerCongr (Matrix.SpecialLinearGroup.toLin_equiv b)).trans SpecialLinearGroup.centerEquivRootsOfUnity)
        g) =
    ↑(Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity g)

Defined in

Mathlib.LinearAlgebra.SpecialLinearGroup

Cited by

0 results in Mathlib

Foundations

Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.FreeModule.FiniteFintypeDecidableEq