 Let G be any Lie group with a closed sub group H and let L be the Lie algebra of G. Since G is a topological transformation group of L by the adjoint action of G,that is , for every formula_7 , and ~formula_8 , we have ,

where formula_11 is the adjoint representation of G , formula_12 is a homomorphism of G into A which is an automorphism group of G and formula_13 is the mapping formula_14 of G into itself.H is a topological transformation group of L and obviously for every u in H, formula_15 is a Lie algebra automorphism.since H is a closed subgroup of a Lie group G, there is a locally trivial principal bundle over X=G/H having H as a structure group.