Discrete inclusions from Cuntz-Pimsner algebras
Abstract
We show that the core inclusion arising from a Cuntz-Pimsner algebra generated by a full, faithful and dualizable correspondence is C*-discrete, and express it as a crossed-product by an action of a tensor category. In particular, we show U H F n ∞ ⊂ O n \mathsf {UHF}_{n^\infty }\subset \mathcal {O}_n , the inclusion of the fixed-point algebra under the gauge symmetry of the Cuntz algebra, is C*-discrete. We describe the dualizable bimodules appearing under this inclusion, including their semisimple decompositions and fusion rules, their Watatani indices and Pimsner-Popa bases, and their sets of cyclic algebraic generators.
Fields of Study & Subjects
Advanced Algebra and Logic
Advanced Banach Space Theory
Advanced Operator Algebra Research
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 154
- Issue
- 4
- Pages
- 1623–1638
- Publication date
- 27 January 2026
- Language
- EN