A Note on Twisted Linear Actions on a Sphere

Abstract

Let G be a Lie group. A TC-pair (ρ,M ) of G gives a twisted linear action on a sphere. Assume that G ⁄kerρ is non-compact. Then the TC-pairs are equivalent, if the corresponding twisted linear actions are coincides with each other. Hence also so, if the corresponding twisted linear actions are transitive and equivariantly diffeomorphic.