Actions of some simple compact Lie groups on themselves


ÇOBANKAYA A. , DÖNMEZ D.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, cilt.129, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 129 Konu: 5
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s12044-019-0502-z
  • Dergi Adı: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES

Özet

Let G be a compact connected simple Lie group acting non-transitively, non-trivially on itself. Hsiang (Cohomology theory of topological transformation groups, (1975) (New York: Springer)) conjectured that the principal isotropy subgroup type must be the maximal torus and the action must be cohomologically similar to the adjoint action and the orbit space must be a simplex. But Bredon (Bull AMS83(4) (1977) 711-718) found a simple counterexample, where the principal isotropy subgroup is not a maximal torus and which has no fixed point. In this work, we prove that if SO(n), (n >= 34) or SU(3) acts smoothly (and nontrivially) on itself with non-empty fixed point set, then the principal isotropy subgroups are maximal tori.