Discrete inclusions from Cuntz-Pimsner algebras
arXiv:2503.21515 · doi:10.1090/proc/17546
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.
This manuscript is an generalization of a split part of the article Discrete Inclusions of C*-algebras [2305.05072v1], which was partitioned and replaced by [2305.05072v2] to better lay out the results therein