SciPost Submission Page
Computing associators of endomorphism fusion categories
by Daniel Barter, Jacob C. Bridgeman, Ramona Wolf
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users): | Jacob C Bridgeman · Ramona Wolf |
Submission information | |
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Preprint Link: | scipost_202204_00039v1 (pdf) |
Code repository: | https://github.com/JCBridgeman/FSymbolsFromModules |
Date accepted: | 2022-07-27 |
Date submitted: | 2022-04-25 10:34 |
Submitted by: | Bridgeman, Jacob C |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
Specialties: |
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Approaches: | Theoretical, Computational |
Abstract
Many applications of fusion categories, particularly in physics, require the associators or $F$-symbols to be known explicitly. Finding these matrices typically involves solving vast systems of coupled polynomial equations in large numbers of variables. In this work, we present an algorithm that allows associator data for some category with unknown associator to be computed from a Morita equivalent category with known data. Given a module category over the latter, we utilize the representation theory of a module tube category, built from the known data, to compute this unknown associator data. When the input category is unitary, we discuss how to ensure the obtained data is also unitary. We provide several worked examples to illustrate this algorithm. In addition, we include several Mathematica files showing how the algorithm can be used to compute the data for the Haagerup category $\mathcal{H}_1$, whose data was previously unknown.
Author comments upon resubmission
List of changes
A collection of minor changes detailed in the response to referees.
Published as SciPost Phys. 13, 029 (2022)
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2022-6-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202204_00039v1, delivered 2022-06-08, doi: 10.21468/SciPost.Report.5203
Report
Dear Authors and Editors,
I would like to thank the authors for their various clarifications, both in the reply to my report, as well as in the resubmitted manuscript. With these changes/clarifications, I recommend publication of the paper in SciPost in the current version.
Anonymous on 2022-05-03 [id 2440]
I thank you the authors for addressing my comments and questions. I am now satisfied with the manuscript to be published.