Homogeneity of the pure state space of the Cuntz algebra

1999/04/30 by Ola Bratteli, Bratteli, Ola, Akitaka Kishimoto +1
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/9904174

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

openalex publication_date 1999/04/30 · arxiv created 1999/05/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

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• Endomorphisms of B(H), extensions of pure states, and a class of representations of O_n
• Homogeneity of the pure state space of a separable C*-algebra
• States of Toeplitz-Cuntz algebras
• Pure states on Cuntz algebras arising from geometric progressions