Theorems · Definition · group theory

Representation.finsuppTensorRight

{G : Type v} →
  [inst : Monoid G] →
    {V : Type v'} →
      [inst_1 : AddCommMonoid V] →
        {W : Type w'} →
          [inst_2 : AddCommMonoid W] →
            {k : Type u} →
              [inst_3 : CommSemiring k] →
                [inst_4 : Module k V] →
                  [inst_5 : Module k W] →
                    (σ : Representation k G V) →
                      (ρ : Representation k G W) →
                        (α : Type w') → [DecidableEq α] → (σ.tprod (ρ.finsupp α)).Equiv ((σ.tprod ρ).finsupp α)

Equiv between representations induced by linear equiv between V ⊗[k] (α →₀ W) and α →₀ (V ⊗[k] W).

Defined in

Mathlib.RepresentationTheory.Equiv

Cited by

4 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidAddCommMonoidAddCommMonoidCommSemiringModuleModuleDecidableEq