Theorems · Definition · group theory

Representation.ofQuotient

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      [inst : Semiring k] →
        [inst_1 : Group G] →
          [inst_2 : AddCommMonoid V] →
            [inst_3 : Module k V] →
              (ρ : Representation k G V) →
                (S : Subgroup G) →
                  [inst_4 : S.Normal] →
                    [Representation.IsTrivial (MonoidHom.comp ρ S.subtype)] → Representation k (G ⧸ S) V

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

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

3 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringGroupAddCommMonoidModuleSubgroup.NormalRepresentation.IsTrivial