Planar algebras
نویسندگان
چکیده

 We introduce a notion of planar algebra, the simplest example which is vector space tensors, closed under contractions. A algebra with suitable positivity properties produces finite index subfactor II1 factor, and vice versa.
منابع مشابه
A2-Planar Algebras II: Planar Modules
Generalizing Jones’s notion of a planar algebra, we have previously introduced an A2-planar algebra capturing the structure contained in the double complex pertaining to the subfactor for a finite SU(3) ADE graph with a flat cell system. We now introduce the notion of modules over an A2-planar algebra, and describe certain irreducible Hilbert A2-TL-modules. We construct an A2-graph planar algeb...
متن کاملSubfactors and Planar Algebras
An inclusion of II1 factors N ⊂ M with finite Jones index gives rise to a powerful set of invariants that can be approached successfully in a number of different ways. We describe Jones’ pictorial description of the standard invariant of a subfactor as a so-called planar algebra and show how this point of view leads to new structure results for subfactors. 2000 Mathematics Subject Classificatio...
متن کاملFree Analysis and Planar Algebras
We study 2-cabled analogs of Voiculescu’s trace and free Gibbs states on Jones planar algebras. These states are traces on a tower of graded algebras associated to a Jones planar algebra. Among our results is that, with a suitable de nition, niteness of free Fisher information for planar algebra traces implies that the associated tower of von Neumann algebras consists of factors, and that the s...
متن کاملA 2 -planar Algebras I
We give a diagrammatic representation of the A2-Temperley-Lieb algebra, and show that it is isomorphic to Wenzl’s representation of a Hecke algebra. Generalizing Jones’s notion of a planar algebra, we construct an A2-planar algebra which will capture the structure contained in the SU(3) ADE subfactors. We show that the subfactor for an ADE graph with a flat connection has a description as a fla...
متن کاملSkein Theory for the D2n Planar Algebras
Abstract We give a combinatorial description of the “D2n planar algebra”, by giving generators and relations. This includes a direct proof that the relations are consistent, as well as a complete description of the associated tensor category and its principal graph. While we use the usual langauge of subfactor planar algebras, the entire argument is ‘skein-theoretic’, and there is no functional...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: New Zealand journal of mathematics
سال: 2021
ISSN: ['1171-6096', '1179-4984']
DOI: https://doi.org/10.53733/172