Theorems · Definition · group theory

Representation.tprod

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        [inst : CommSemiring k] →
          [inst_1 : Monoid G] →
            [inst_2 : AddCommMonoid V] →
              [inst_3 : Module k V] →
                [inst_4 : AddCommMonoid W] →
                  [inst_5 : Module k W] →
                    Representation k G V → Representation k G W → Representation k G (TensorProduct k V W)

Given representations of G on V and W, there is a natural representation of G on their tensor product V ⊗[k] W.

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

103 results in Mathlib

Foundations

Depth 65 from the axioms, rests on 935 definitions · uses propext, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModuleAddCommMonoidModule