asAlgebraHom — Mathlib

English

A representation ρ yields a k-algebra homomorphism from MonoidAlgebra(k,G) to End_k(V).

Русский

Представление ρ задаёт гомоморфизм алгебр над-k от MonoidAlgebra(k,G) в End_k(V).

LaTeX

$$ρ.asAlgebraHom : MonoidAlgebra k G →ₐ[k] End_k(V)$$

Lean4

/-- A `k`-linear representation of `G` on `V` can be thought of as
an algebra map from `MonoidAlgebra k G` into the `k`-linear endomorphisms of `V`.
-/
noncomputable def asAlgebraHom : MonoidAlgebra k G →ₐ[k] Module.End k V :=
  (lift k G _) ρ

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