Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six
This paper classifies the Grothendieck rings of complex fusion categories of multiplicity one
up to rank six. Among 72 possible fusion rings, 25 ones are filtered out by using …
up to rank six. Among 72 possible fusion rings, 25 ones are filtered out by using …
Unitary dual functors for unitary multitensor categories
D Penneys - arXiv preprint arXiv:1808.00323, 2018 - arxiv.org
We classify which dual functors on a unitary multitensor category are compatible with the
dagger structure in terms of groupoid homomorphisms from the universal grading groupoid …
dagger structure in terms of groupoid homomorphisms from the universal grading groupoid …
A Cuntz algebra approach to the classification of near-group categories
M Izumi - Proceedings of the 2014 Maui and, 2015 - projecteuclid.org
A. We classify C∗ near-group categories by using Vaughan Jones theory of subfactors and
the Cuntz algebra endomorphisms. Our results show that there is a sharp contrast between …
the Cuntz algebra endomorphisms. Our results show that there is a sharp contrast between …
[图书][B] The Classification of Subfactors with Index at Most 5\frac {1} 4
N Afzaly, S Morrison, D Penneys - 2023 - ams.org
Subfactor standard invariants encode quantum symmetries. The small index subfactor
classification program has been a rich source of interesting quantum symmetries. We give …
classification program has been a rich source of interesting quantum symmetries. We give …
[HTML][HTML] Pseudo-unitary non-self-dual fusion categories of rank 4
HK Larson - Journal of Algebra, 2014 - Elsevier
A fusion category of rank 4 has either four self-dual simple objects or exactly two self-dual
simple objects. We study fusion categories of rank 4 with exactly two self-dual simple …
simple objects. We study fusion categories of rank 4 with exactly two self-dual simple …
The classification of subfactors with index at most
N Afzaly, S Morrison, D Penneys - arXiv preprint arXiv:1509.00038, 2015 - arxiv.org
Subfactor standard invariants encode quantum symmetries. The small index subfactor
classification program has been a rich source of interesting quantum symmetries. We give …
classification program has been a rich source of interesting quantum symmetries. We give …
Infinite families of potential modular data related to quadratic categories
P Grossman, M Izumi - Communications in Mathematical Physics, 2020 - Springer
We present several infinite families of potential modular data motivated by examples of
Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric …
Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric …
Yang-Baxter relation planar algebras
Z Liu - arXiv preprint arXiv:1507.06030, 2015 - arxiv.org
We give a new type of Schur-Weyl duality for the representations of a family of quantum
subgroups and their centralizer algebra. We define and classify singly-generated, Yang …
subgroups and their centralizer algebra. We define and classify singly-generated, Yang …
Complete Positivity of Comultiplication and Primary Criteria for Unitary Categorification
In this paper, we investigate quantum Fourier analysis on subfactors and unitary fusion
categories. We prove the complete positivity of the comultiplication for subfactors and derive …
categories. We prove the complete positivity of the comultiplication for subfactors and derive …
Subfactors of index exactly 5
M Izumi, S Morrison, D Penneys… - Bulletin of the London …, 2015 - academic.oup.com
We give the classification of subfactor planar algebras at index exactly 5. All the examples
arise as standard invariants of subgroup subfactors. Some of the requisite uniqueness …
arise as standard invariants of subgroup subfactors. Some of the requisite uniqueness …