Homogeneity of the Pure State Space of the Cuntz Algebra
by
Ola Bratteli
University of Oslo
Coauthors: Akitaka Kishimoto

We prove that the automorphism group of a Cuntz algebra of finite order acts transitively on the set of pure states which are invariant under some gauge action (which may depend on the states). The question of whether any pure state is invariant under some gauge action is left open, but for the semigroups of unital endomorphisms stronger transitivity properties can be established without knowing the answer of this question.

Date received: May 8, 1999