Homogeneity of the pure state space of the Cuntz algebra

Details Homogeneity of the pure state space of the Cuntz algebra Homogeneity of the pure state space of the Cuntz algebra

1999-04-30

arxiv.org/abs/math/9904174v2

Mathematics

Operator Algebras

11 pages, latex. Correction in the new version: In Corollary 1 and the preceding remarks one must assume that d is a power of

Scientific paper

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 actions (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 senigroups of unital endomorphisms stronger transitivity properties can be established witout knowing the answer of this question.

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