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arXiv · 2503.21515

Discrete inclusions from Cuntz-Pimsner algebras

Roberto Hernández Palomares
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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 unitary tensor category. In particular, we show the inclusion of the UHF subalgebra of the Cuntz algebra arising as the fixed-point subalgebra under the gauge symmetry, is irreducible and 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, as well as their sets of cyclic algebraic generators.

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Roberto Hernández Palomares. 2025-03-27. Discrete inclusions from Cuntz-Pimsner algebras. https://doi.org/10.1090/proc%2F17546

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