Pith. sign in

REVIEW 5 cited by

Arveson's hyperrigidity conjecture is false

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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 2404.05018 v2 pith:S6ZZUGBN submitted 2024-04-07 math.OA math.FA

Boris Bilich , Adam Dor-On This is my paper · ORCID
classification math.OAmath.FA
keywords mathcalconjecturealgebraarvesongeneratedhyperrigidityoperatorboundary
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

Arveson's hyperrigidity conjecture predicts that if the non-commutative Choquet boundary of a separable operator system $\mathcal{S}$ is the entire spectrum of its generated C*-algebra $\mathcal{B}$ then $\mathcal{S}$ is hyperrigid in $\mathcal{B}$. We provide a counterexample to the conjecture with a C*-algebra $\mathcal{B}$ of type I generated by a single operator.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

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

  1. The Hyperrigidity Conjecture for compact convex sets in $\mathbb{R}^2$

    math.FA 2024-11 conditional novelty 8.0 of 10

    The affine function space on any compact convex planar set is hyperrigid in the C*-algebra of continuous functions on the extreme points.

  2. The Hao-Ng isomorphism theorem for reduced crossed products

    math.OA 2025-05 conditional novelty 7.0 of 10

    For any C*-correspondence with a generalized gauge action by a locally compact Hausdorff group, the Cuntz-Pimsner algebra of the reduced crossed product is canonically isomorphic to the reduced crossed product of the ...

  3. A Finite Dimensional Counterexample for Arveson's Hyperrigidity Conjecture

    math.FA 2025-02 conditional novelty 7.0 of 10

    For each 0<c<1, the operator system generated by four concrete operators on L2(S3)⊕C is not hyperrigid, while every irreducible representation of its C*-algebra restricts to a boundary representation.

  4. $C^*$-supports and abnormalities of operator systems

    math.OA 2025-01 accept novelty 6.0 of 10

    C*-supports are unique exactly when the generated C*-algebra lies in every injective envelope, yielding new characterizations of unique extension and hyperrigidity and a formula for the span of abnormalities.

  5. Hyperrigidity III

    math.OA 2024-12 conditional novelty 6.0 of 10

    In a unital separable C*-algebra, a set G is hyperrigid exactly when every sequence of representations that converges weakly on G converges strongly on the whole algebra.

Pith tools