Theorems · Theorem · group theory

Representation.asModuleEquiv_symm_map_rho

∀ {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) (g : G) (x : V),
  ρ.asModuleEquiv.symm ((ρ g) x) = (MonoidAlgebra.of k G) g • ρ.asModuleEquiv.symm x

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule