Theorems · Theorem · group theory

Representation.ofQuotient_coe_apply

∀ {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]
  [inst_5 : Representation.IsTrivial (MonoidHom.comp ρ S.subtype)] (g : G) (x : V), ((ρ.ofQuotient S) ↑g) x = (ρ g) x

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

SemiringGroupAddCommMonoidModuleSubgroup.NormalRepresentation.IsTrivial