asModuleEquiv — Mathlib

English

The self-inverse action relation ρ g (ρ g^{-1} x) = x holds for all g ∈ G and x ∈ V.

Русский

Отношение самоконсервируемого действия: ρ g (ρ g^{-1} x) = x для всех g ∈ G и x ∈ V.

LaTeX

$$ρ g (ρ g^{-1} x) = x$$

Lean4

/-- The additive equivalence from the `Module (MonoidAlgebra k G)` to the original vector space
of the representative.

This is just the identity, but it is helpful for typechecking and keeping track of instances.
-/
def asModuleEquiv : ρ.asModule ≃ₗ[k] V :=
  LinearEquiv.refl _ _

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