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Title: Classification of rank 5 premodular categories

Journal Article · · Journal of Mathematical Physics
DOI:https://doi.org/10.1063/1.5020256· OSTI ID:1511176

We survey a number of classification tools developed in recent years and employ them to classify pseudounitary rank 5 premodular categories up to Grothendieck equivalence.

Research Organization:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC05-76RL01830; PNNL-SA-120942
OSTI ID:
1511176
Alternate ID(s):
OSTI ID: 1421110
Report Number(s):
PNNL-SA-120942
Journal Information:
Journal of Mathematical Physics, Vol. 59, Issue 1; ISSN 0022-2488
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

References (31)

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(3+1)-TQFTs and topological insulators journal July 2011
On Classification of Modular Categories by Rank: Table A.1 journal April 2016
Rank-finiteness for modular categories journal July 2015
On the classification of weakly integral modular categories journal June 2016
Weakly group-theoretical and solvable fusion categories journal January 2011
On braided fusion categories I journal March 2010
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padding-left: 0; line-height:1.8em;"> <li class="authors">Müger, Michael</li> <li class="mb-0-5 source"> <span class="mr-1">Proceedings of the London Mathematical Society, Vol. 87, Issue 02</span> <span class="text-muted"><a href="https://doi.org/10.1112/s0024611503014187" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1112/s0024611503014187<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2003-09-01">September 2003</span></td> </tr><tr> <td> <a href="https://doi.org/10.17323/1609-4514-2002-2-2-227-248" target="_blank" rel="noopener noreferrer" class="title" data-title="Categories Tensorielles">Categories Tensorielles<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; 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padding-left: 0; line-height:1.8em;"> <li class="authors">Drinfeld, Vladimir; Gelaki, Shlomo; Nikshych, Dmitri</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.0906.0620" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.0906.0620<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="preprint">preprint</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2009-01-01">January 2009</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1012.0814" target="_blank" rel="noopener noreferrer" class="title" data-title="Modular categories integrality and Egyptian fractions">Modular categories, integrality and Egyptian fractions<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; 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padding-left: 0; line-height:1.8em;"> <li class="authors">Walker, Kevin; Wang, Zhenghan</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1104.2632" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1104.2632<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="preprint">preprint</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2011-01-01">January 2011</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.cond-mat/0506438" target="_blank" rel="noopener noreferrer" class="title" data-title="Anyons in an exactly solved model and beyond">Anyons in an exactly solved model and beyond<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Kitaev, Alexei</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.cond-mat/0506438" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.cond-mat/0506438<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2005-01-01">January 2005</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.math/0610726" target="_blank" rel="noopener noreferrer" class="title" data-title="Nilpotent fusion categories">Nilpotent fusion categories<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Gelaki, Shlomo; Nikshych, Dmitri</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.math/0610726" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.math/0610726<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2006-01-01">January 2006</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.0809.3031" target="_blank" rel="noopener noreferrer" class="title" data-title="Weakly grouptheoretical and solvable fusion categories">Weakly group-theoretical and solvable fusion categories<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Etingof, Pavel; Nikshych, Dmitri; Ostrik, Victor</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.0809.3031" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.0809.3031<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="preprint">preprint</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2008-01-01">January 2008</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1507.05139" target="_blank" rel="noopener noreferrer" class="title" data-title="On classification of modular categories by rank">On classification of modular categories by rank<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Bruillard, Paul; Ng, Siu-Hung; Rowell, Eric C.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1507.05139" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1507.05139<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="preprint">preprint</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2015-01-01">January 2015</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.hep-th/9409028" target="_blank" rel="noopener noreferrer" class="title" data-title="Quantum Invariants of Knots and 3Manifolds">Quantum Invariants of Knots and 3-Manifolds<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Turaev, V.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.hep-th/9409028" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.hep-th/9409028<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="preprint">preprint</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="1994-01-01">January 1994</span></td> </tr></tbody></table> </div> </div> </section> <hr class="mt-2 mb-2"/> <section id="section-similar" class="tab-content-sec osti-curated biblio-section section-scroll" style="scroll-margin-top:110px;"> <div class="row"> <div class="col-8" style="padding-right:40px;"> <h2 class="abstract">Similar Records</h2> <div class="" style="line-height:1.6rem;"> <a href="/biblio/1340755" target="_blank">Rank 4 Premodular Categories</a> <div class="small" style="line-height:1.4rem;"> Journal Article <span style="padding-left: 0.75rem;padding-right: 0.75rem;">·</span> Thu Sep 01 00:00:00 EDT 2016 <span style="padding-left: 0.75rem;padding-right: 0.75rem;">·</span> New York Journal of Mathematics, 22:775-800 <span style="padding-left: 0.75rem;padding-right: 0.75rem;">·</span> <span class="text-muted" style="padding-right:0.5em;">OSTI ID:</span>1511176 </div> <div class="small" style="line-height:1.4rem;"> <span class="author-link"><a href="/search/author:"Bruillard, Paul J."" class="btn btn-link btn-sm"><span class="author" itemprop="author">Bruillard, Paul J.; 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