Theorems · Definition · group theory

Representation.mapSubmodule

{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) → ↥ρ.invtSubmodule ≃o Submodule (MonoidAlgebra k G) ρ.asModule

The natural order isomorphism between the two ways to represent invariant submodules.

Defined in

Mathlib.RepresentationTheory.Submodule

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule