Theorems · Theorem · group theory

Representation.ofModule_asAlgebraHom_apply_apply

∀ {k : Type u_1} {G : Type u_2} [inst : CommSemiring k] [inst_1 : Monoid G] (M : Type u_4) [inst_2 : AddCommMonoid M]
  [inst_3 : Module (MonoidAlgebra k G) M] (r : MonoidAlgebra k G) (m : RestrictScalars k (MonoidAlgebra k G) M),
  ((Representation.ofModule M).asAlgebraHom r) m =
    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm (r • (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule