Bazi basit Lie gruplarinin kendi üzerine etkisi

Let G be a compact connected simple Lie group and let it act non-transitively, non-trivially on itself. Hsiang (1975), conjectured that the principal isotropy subgroup type must be the maximal torus and the action must be cohomologically similar that of the adjoint action. But Bredon (1977), with a simple counyrexample, showed that this idea is false. In this work, we define adjoint-like action and we prove that if SO(n), (n>7) or SU(3) acts smoothly (and nontrivially) on itself with non-empty fixed point set, then the action is adjoint-like.