Theorems · Definition · group theory

Representation.dual

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      [inst : CommSemiring k] →
        [inst_1 : Group G] →
          [inst_2 : AddCommMonoid V] →
            [inst_3 : Module k V] → Representation k G V → Representation k G (Module.Dual k V)

The dual of a representation ρ of G on a module V, given by (dual ρ) g f = f ∘ₗ (ρ g⁻¹), where f : Module.Dual k V.

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

9 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringGroupAddCommMonoidModule