$C^*$-simplicity for groups with non-elementary convergence group   actions
  We prove that a countable group with an effective minimal non-elementary convergence group action is a Powers group. More strongly we prove that it is a strongly Powers group and thus its non-trivial subnormal subgroups are $C^*$-simple. 
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
math.OA math.DS math.GR