Modular categories of dimension $p^3m$ with $m$ square-free
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- by Paul Bruillard, Julia Yael Plavnik and Eric C. Rowell PDF
- Proc. Amer. Math. Soc. 147 (2019), 21-34 Request permission
Abstract:
We give a complete classification of modular categories of dimension $p^3m$ where $p$ is prime and $m$ is a square-free integer relatively prime to $p$. When $p$ is odd, all such categories are pointed. For $p=2$ one encounters modular categories with the same fusion ring as orthogonal quantum groups at certain roots of unity, namely $\mathrm {SO}(2m)_2$. We also classify the more general class of modular categories with the same fusion rules as $\mathrm {SO}(2N)_2$ with $N$ odd.References
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Additional Information
- Paul Bruillard
- Affiliation: Pacific Northwest National Laboratory, Richland, Washington 99354
- MR Author ID: 893733
- Email: Paul.Bruillard@pnnl.gov
- Julia Yael Plavnik
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 990893
- Email: julia@math.tamu.edu
- Eric C. Rowell
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 752263
- Email: rowell@math.tamu.edu
- Received by editor(s): October 4, 2016
- Received by editor(s) in revised form: April 4, 2017
- Published electronically: October 19, 2018
- Additional Notes: The authors thank Yu Tsumura for his comments, and César Galindo for useful discussions
The second and third authors were partially supported by NSF grant DMS-1410144. The second author would like to thank the Association of Women in Mathematics for the AWM grant. Some of the results in this paper were obtained while the authors were at the American Institute of Mathematics during May 2016, participating in a SQuaRE. They would like to thank AIM for its hospitality and encouragement. The research in this paper was, in part, conducted under the Laboratory Directed Research and Development Program at PNNL, a multi-program national laboratory operated by Battelle for the U.S. Department of Energy - Communicated by: Kailash Misra
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 21-34
- MSC (2010): Primary 18D10; Secondary 16T05
- DOI: https://doi.org/10.1090/proc/13776
- MathSciNet review: 3876728