smulLeft — Mathlib

English

The symmetric version acts on n with (piCongrRight f).symm n i = (f(i)).symm(n(i)).

Русский

Симметричный вариант действует на n так, что (piCongrRight f).symm n i = (f(i)).symm(n(i)).

LaTeX

$$$(\\text{piCongrRight}\ f)\\.symm\\ n\\ i = (f(i))\\,^{-1}(n(i))$$$

Lean4

/-- Scalar multiplication by a group element as a continuous linear equivalence. -/
@[simps! apply_toLinearEquiv apply_apply]
def smulLeft : G →* M₁ ≃L[R₁] M₁
    where
  toFun g := ⟨DistribMulAction.toModuleAut _ _ g, continuous_const_smul _, continuous_const_smul _⟩
  map_mul' _ _ := toLinearEquiv_injective <| map_mul (DistribMulAction.toModuleAut _ _) _ _
  map_one' := toLinearEquiv_injective <| map_one <| DistribMulAction.toModuleAut _ _

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