coevaluation — Mathlib

English

The star map on the Clifford algebra sends the image of a vector m ∈ M under ι to its negative.

Русский

Звезда отображения ι_Q(m) отправляет в -ι_Q(m).

LaTeX

$$star (ι_Q(m)) = -ι_Q(m).$$

Lean4

/-- The coevaluation map is a linear map from a field `K` to a finite-dimensional
  vector space `V`. -/
def coevaluation : K →ₗ[K] V ⊗[K] Module.Dual K V :=
  let bV := Basis.ofVectorSpace K V
  (Basis.singleton Unit K).constr K fun _ => ∑ i : Basis.ofVectorSpaceIndex K V, bV i ⊗ₜ[K] bV.coord i

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