Remarks on C*-discrete inclusions
Abstract
We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality condition. Furthermore, we define freeness for actions of tensor categories on C*-algebras, and show simplicity is preserved under taking reduced crossed products. Finally, we show under certain constraints that A-valued semicircular systems give rise to C*-discrete inclusions, and thus are crossed products by an action of a tensor category. Along the way, we show the set of single algebraic generators of a dualizable bimodule forms an open subset.
Keywords
Cite
@article{arxiv.2409.18161,
title = {Remarks on C*-discrete inclusions},
author = {Roberto Hernández Palomares and Brent Nelson},
journal= {arXiv preprint arXiv:2409.18161},
year = {2026}
}
Comments
This is a split part of the article Discrete Inclusions of C*-algebras [2305.05072v1] by the same authors, which was partitioned and replaced by [2305.05072v2] to better lay out the results therein Version 2 incorporates a corrected statement and proof of Theorem A which now highlights the importance of traciality for algebra objects. (To appear at the Journal of Noncommutative Geometry)