Finite order automorphisms and dimension groups of Cantor minimal systems

Abstract

We compute the dimension group of the skew product extension of a Cantor minimal system associated with a finite group valued cocycle. Using it, we study finite subgroups in the commutant group of a Cantor minimal system and prove that a finite subgroup of the kernel of the mod map must be cyclic. Moreover, we give a certain obstruction for finite subgroups of commutant groups to have non-zero intersection to the kernel of mod maps. We also give a necessary and sufficient condition for dimension groups so that the kernel of the mod map can include a finite order element.