addInvariantVectorField_smul — Mathlib

English

Pullback of mulInvariantVectorField along left-multiplication by g leaves it unchanged: mpullback I I (g * ·) (mulInvariantVectorField v) = mulInvariantVectorField v.

Русский

Вытягивание взад вдоль левой умножения на g не изменяет mulInvariantVectorField.

LaTeX

$$$mpullback I I (g*\\cdot) (mulInvariantVectorField v) = mulInvariantVectorField v$$$

Lean4

theorem addInvariantVectorField_smul {G : Type*} [TopologicalSpace G] [ChartedSpace H G] [AddGroup G] (c : 𝕜)
    (v : AddGroupLieAlgebra I G) : addInvariantVectorField (c • v) = c • addInvariantVectorField v :=
  by
  ext g
  simp [addInvariantVectorField]

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