Theorems · Definition · group theory

Representation.IntertwiningMap.centralMul

{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) → (g : G) → g ∈ Submonoid.center G → ρ.IntertwiningMap ρ

If g is a central element of a monoid G, then this is the action of g, considered as an intertwining map from any representation of G to itself.

Defined in

Mathlib.RepresentationTheory.Intertwining

Cited by

0 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule