Pith. sign in

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

arxiv 2405.18429 v4 pith:SDEP62SC submitted 2024-05-28 math.OA math.KTmath.QA

classification math.OAmath.KTmath.QA
keywords algebrastensorunitaryactionscategorieskirchbergcategorycuntz
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ergodic automorphisms on Kirchberg algebras

    math.OA 2025-05 conditional novelty 8.0 of 10

    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.

  2. Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras

    math.OA 2026-05 unverdicted novelty 7.0 of 10

    Stabilized Cuntz–Pimsner algebras decompose as crossed products, yielding new classifications of simplicity, ideals, traces, KMS weights, and quasi-free crossed products.

Pith tools