starHom — Mathlib

English

The star operation induces a canonical algebra isomorphism between FreeAlgebra(R,X) and its opposite: FreeAlgebra(R,X) ≃ₐ[R] (FreeAlgebra(R,X))ᵐᵒᵖ.

Русский

Операция звезды задаёт каноническое алгебраическое изоморфизм между FreeAlgebra(R,X) и её противоположностью.

LaTeX

$$$\text{FreeAlgebra}(R,X) \cong_{\!\!R} (\text{FreeAlgebra}(R,X))^{\mathrm{op}}$$$

Lean4

/-- `star` as an `AlgEquiv` -/
def starHom : FreeAlgebra R X ≃ₐ[R] (FreeAlgebra R X)ᵐᵒᵖ :=
  { starRingEquiv with commutes' := fun r => by simp [star_algebraMap] }

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