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]