Theorems · Inductive type · Lie groups

LeftInvariantDerivation

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type u_3} →
            [inst_3 : TopologicalSpace H] →
              (I : ModelWithCorners 𝕜 E H) →
                (G : Type u_4) →
                  [inst_4 : TopologicalSpace G] →
                    [inst_5 : ChartedSpace H G] → [inst_6 : Monoid G] → [ContMDiffMul I (↑⊤) G] → Type (max u_1 u_4)

Left-invariant global derivations. A global derivation is left-invariant if it is equal to its pullback along left multiplication by an arbitrary element of G.

Defined in

Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation

Cited by

33 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceMonoidContMDiffMul