Theorems · Theorem · Lie groups

mulInvariantVectorField_eq_mpullback

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {G : Type u_4}
  [inst_4 : TopologicalSpace G] [inst_5 : ChartedSpace H G] [inst_6 : Group G] [LieGroup I (minSmoothness 𝕜 3) G]
  (g : G) (V : (g : G) → TangentSpace I g),
  mulInvariantVectorField (V 1) g = VectorField.mpullback I I (fun x => g⁻¹ * x) V g

Defined in

Mathlib.Geometry.Manifold.GroupLieAlgebra

Cited by

1 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceGroupLieGroup