Theorems · Definition · group theory

Rep.resOfQuotientIso

{k : Type u} →
  [inst : Semiring k] →
    {G : Type v} →
      [inst_1 : Group G] →
        (A : Rep.{u_1, u, v} k G) →
          (S : Subgroup G) →
            [inst_2 : S.Normal] →
              [inst_3 : Representation.IsTrivial (MonoidHom.comp A.ρ S.subtype)] →
                Rep.res (QuotientGroup.mk' S) (A.ofQuotient S) ≅ A

A G-representation A on which a normal subgroup S ≤ G acts trivially induces a G ⧸ S-representation on A, and composing this with the quotient map G → G ⧸ S gives the original representation by definition. Useful for typechecking.

Defined in

Mathlib.RepresentationTheory.Rep.Res

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringGroupSubgroup.NormalRepresentation.IsTrivial