Theorems · Theorem · group theory

Representation.asModuleEquiv_map_smul

∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommSemiring k] [inst_1 : Monoid G] [inst_2 : AddCommMonoid V]
  [inst_3 : Module k V] (ρ : Representation k G V) (r : MonoidAlgebra k G) (x : ρ.asModule),
  ρ.asModuleEquiv (r • x) = (ρ.asAlgebraHom r) (ρ.asModuleEquiv x)

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule