Theorems · Definition · group theory

Representation.IntertwiningMap.equivAlgEnd

{A : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      [inst : CommSemiring A] →
        [inst_1 : Monoid G] →
          [inst_2 : AddCommMonoid V] →
            [inst_3 : Module A V] →
              (ρ : Representation A G V) → ρ.IntertwiningMap ρ ≃ₐ[A] Module.End (MonoidAlgebra A G) ρ.asModule

Intertwining maps from ρ to itself are the same as A[G]-linear endomorphisms.

Defined in

Mathlib.RepresentationTheory.Intertwining

Cited by

1 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule