REVIEW 2 cited by
Actions of tensor categories on Kirchberg algebras
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We characterize the simplicity of Pimsner algebras for non-proper C*-correspondences. With the aid of this criterion, we give a systematic strategy to produce outer actions of unitary tensor categories on Kirchberg algebras. In particular, every countable unitary tensor category admits an outer action on the Cuntz algebra $\mathcal{O}_2$. We also study the realizability of modules over fusion rings as K-groups of Kirchberg algebras acted on by unitary tensor categories, which turns out to be generically true for every unitary fusion category. Several new examples are provided, among which actions on Cuntz algebras of 3-cocycle twists of cyclic groups are constructed for all possible 3-cohomological classes, thereby answering a question asked by Izumi.
Forward citations
Cited by 2 Pith papers
-
Ergodic automorphisms on Kirchberg algebras
Every countable infinite discrete group admits an ergodic action on any unital Kirchberg algebra, and every aperiodic automorphism of such an algebra has a unitary perturbation that is ergodic.
-
Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras
Stabilized Cuntz–Pimsner algebras decompose as crossed products, yielding new classifications of simplicity, ideals, traces, KMS weights, and quasi-free crossed products.
Discussion (0). Continue with ORCID to comment.