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 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.