Theorems · Definition · group theory

Representation.IntertwiningMap.equivLinearMapAsModule

{A : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        [inst : CommSemiring A] →
          [inst_1 : Monoid G] →
            [inst_2 : AddCommMonoid V] →
              [inst_3 : AddCommMonoid W] →
                [inst_4 : Module A V] →
                  [inst_5 : Module A W] →
                    (ρ : Representation A G V) →
                      (σ : Representation A G W) → ρ.IntertwiningMap σ ≃ₗ[A] ρ.asModule →ₗ[MonoidAlgebra A G] σ.asModule

An intertwining map is the same thing as a linear map over the group ring.

Defined in

Mathlib.RepresentationTheory.Intertwining

Cited by

3 results in Mathlib

Foundations

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

Assumes

CommSemiringMonoidAddCommMonoidAddCommMonoidModuleModule