Theorems · Definition · group theory

Representation.toCoinvariants

{k : Type u_6} →
  {G : Type u_7} →
    {V : Type u_8} →
      [inst : CommRing k] →
        [inst_1 : Group G] →
          [inst_2 : AddCommGroup V] →
            [inst_3 : Module k V] →
              (ρ : Representation k G V) →
                (S : Subgroup G) →
                  [S.Normal] → Representation k G (Representation.Coinvariants (MonoidHom.comp ρ S.subtype))

Given a normal subgroup S ≤ G, a G-representation ρ induces a G-representation on the coinvariants of ρ|_S.

Defined in

Mathlib.RepresentationTheory.Coinvariants

Cited by

2 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupAddCommGroupModuleSubgroup.Normal