Theorems · Definition · Lie groups

addInvariantVectorField

{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 : AddGroup G] → AddGroupLieAlgebra I G → (g : G) → TangentSpace I g

The invariant vector field associated to a vector v in the Lie algebra. At a point g, it is given by the image of v under left-addition by g.

Defined in

Mathlib.Geometry.Manifold.GroupLieAlgebra

Cited by

10 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceAddGroup