Reductions of Tensor Categories Modulo Primes
Original manuscript February 12, 2011
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Taylor & Francis
2013
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| Online Access: | http://hdl.handle.net/1721.1/80866 https://orcid.org/0000-0002-0710-1416 |
| _version_ | 1826206095499067392 |
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| author | Gelaki, Shlomo Etingof, Pavel I. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Gelaki, Shlomo Etingof, Pavel I. |
| author_sort | Gelaki, Shlomo |
| collection | MIT |
| description | Original manuscript February 12, 2011 |
| first_indexed | 2024-09-23T13:24:01Z |
| format | Article |
| id | mit-1721.1/80866 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:24:01Z |
| publishDate | 2013 |
| publisher | Taylor & Francis |
| record_format | dspace |
| spelling | mit-1721.1/808662022-10-01T15:00:55Z Reductions of Tensor Categories Modulo Primes Gelaki, Shlomo Etingof, Pavel I. Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I. Original manuscript February 12, 2011 We study good (i.e., semisimple) reductions of semisimple rigid tensor categories modulo primes. A prime p is called good for a semisimple rigid tensor category C if such a reduction exists (otherwise, it is called bad). It is clear that a good prime must be relatively prime to the Müger squared norm |V|[superscript 2] of any simple object V of C. We show, using the Ito–Michler theorem in finite group theory, that for group-theoretical fusion categories, the converse is true. While the converse is false for general fusion categories, we obtain results about good and bad primes for many known fusion categories (e.g., for Verlinde categories). We also state some questions and conjectures regarding good and bad primes. National Science Foundation (U.S.) (Grant DMS-1000113) United States-Israel Binational Science Foundation (Grant 2008164) 2013-09-23T16:08:26Z 2013-09-23T16:08:26Z 2011-12 2010-11 Article http://purl.org/eprint/type/JournalArticle 0092-7872 1532-4125 http://hdl.handle.net/1721.1/80866 Etingof, Pavel, and Shlomo Gelaki. “Reductions of Tensor Categories Modulo Primes.” Communications in Algebra 39, no. 12 (December 2011): 4634-4643. https://orcid.org/0000-0002-0710-1416 en_US http://dx.doi.org/10.1080/00927872.2011.617267 Communications in Algebra Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Taylor & Francis arXiv |
| spellingShingle | Gelaki, Shlomo Etingof, Pavel I. Reductions of Tensor Categories Modulo Primes |
| title | Reductions of Tensor Categories Modulo Primes |
| title_full | Reductions of Tensor Categories Modulo Primes |
| title_fullStr | Reductions of Tensor Categories Modulo Primes |
| title_full_unstemmed | Reductions of Tensor Categories Modulo Primes |
| title_short | Reductions of Tensor Categories Modulo Primes |
| title_sort | reductions of tensor categories modulo primes |
| url | http://hdl.handle.net/1721.1/80866 https://orcid.org/0000-0002-0710-1416 |
| work_keys_str_mv | AT gelakishlomo reductionsoftensorcategoriesmoduloprimes AT etingofpaveli reductionsoftensorcategoriesmoduloprimes |