2024/08/19 by Aaron Kettner, Kettner, Aaron · 2 citations
Mathematics · Physics and Astronomy · #37A55 #46L08 #46L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2408.10047
openalex publication_date 2024/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We associate a C^*-algebra to a partial action of the integers acting on the base space of a vector bundle, using the framework of Cuntz--Pimsner algebras. We investigate the structure of the fixed point algebra under the canonical gauge action, and show that it arises from a continuous field of C^*-algebras over the base space, generalising results of Vasselli. We also analyse the ideal structure, and show that for a free action, ideals correspond to open invariant subspaces of the base space. This shows that if the action is free and minimal, then the Cuntz--Pimsner algebra is simple. In the case of a line bundle, we establish a bijective corrrespondence between tracial states on the algebra and invariant measures on the base space. This generalizes results about the C^*-algebras associated to homeomorphisms twisted by vector bundles of Adamo, Archey, Forough, Georgescu, Jeong, Strung and Viola.