Theorems · Definition · group theory

Representation.prod

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        [inst : Semiring 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 (V × W)

Given representations of G on V and W, there is a natural representation of G on their product V × W.

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

17 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

SemiringMonoidAddCommMonoidModuleAddCommMonoidModule