Theorems · Definition · group theory

Rep.ofQuotient

{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] → [Representation.IsTrivial (MonoidHom.comp A.ρ S.subtype)] → Rep.{u_1, u, v} k (G ⧸ S)

Given a normal subgroup S ≤ G, a G-representation ρ which is trivial on S factors through G ⧸ S.

Defined in

Mathlib.RepresentationTheory.Rep.Res

Cited by

4 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringGroupSubgroup.NormalRepresentation.IsTrivial