Theorems · Definition · group theory

SpecialLinearGroup.centerEquivRootsOfUnity

{R : Type u_1} →
  {V : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : AddCommGroup V] →
        [inst_2 : Module R V] →
          [Module.Free R V] →
            [Module.Finite R V] →
              ↥(Subgroup.center (SpecialLinearGroup R V)) ≃* ↥(rootsOfUnity (max (Module.finrank R V) 1) R)

The isomorphism between the roots of unity and the center of the special linear group.

Defined in

Mathlib.LinearAlgebra.SpecialLinearGroup

Cited by

6 results in Mathlib

Foundations

Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.FreeModule.Finite