Pith. sign in

REVIEW 5 cited by

Planar algebras, I

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 math/9909027 v1 pith:K6ND5RNV submitted 1999-09-04 math.QA math.OA

Vaughan F. R. Jones (UC Berkeley) This is my paper · ORCID
classification math.QAmath.OA
keywords planaralgebraalgebrasclosedcontractionsexamplefactorfinite
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II_1 factor, and vice versa.

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. Classification of exchange relation planar algebras through sieving forest fusion graphs

    math.OA 2024-12 conditional novelty 8.0 of 10

    Exchange relation planar algebras are characterized by forest fusion graphs, and this characterization yields a computer-assisted classification of all 5-dimensional subfactorizable fusion bialgebras.

  2. Fusion in the periodic Temperley-Lieb algebra: general definition of a bifunctor

    math-ph 2025-09 accept novelty 7.0 of 10

    A fusion bifunctor on families of modules over the enlarged periodic Temperley-Lieb algebra is constructed and proven associative, commutative, distributive, and unital.

  3. Alterfold Theory and Topological Modular Invariance

    math.QA 2024-12 conditional novelty 6.0 of 10

    Alterfold TQFT gives a unified topological proof framework for modular invariants, alpha-induction, and flat connections, plus new higher-genus and multi-context invariants.

  4. Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules

    math-ph 2019-08 conditional novelty 6.0 of 10

    The Temperley-Lieb-Jones C*-tensor categories at discrete parameters are realized as braided C*-tensor categories of Hilbert C*-modules with finite orthonormal bases.

  5. Irreducibility of the Wysiwyg representations of Thompson's groups

    math.OA 2019-06 unverdicted novelty 6.0 of 10

    Proves irreducibility and mutual inequivalence of Wysiwyg unitary representations of Thompson's groups F and T.

Pith tools