p-adic dimensions in symmetric tensor categories in characteristic p
To every object X of a symmetric tensor category over a field of characteristic p > 0 we attach p-adic integers Dim+(X) and Dim−(X) whose reduction modulo p is the categorical dimension dim(X) of X, coinciding with the usual dimension when X is a vector space. We study properties of Dim±(X), and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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European Mathematical Publishing House
2020
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| Online Access: | https://hdl.handle.net/1721.1/124324 |
| _version_ | 1826198999847141376 |
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| author | Etingof, Pavel I Harman, Nate Ostrik, Victor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I Harman, Nate Ostrik, Victor |
| author_sort | Etingof, Pavel I |
| collection | MIT |
| description | To every object X of a symmetric tensor category over a field of characteristic p > 0 we attach p-adic integers Dim+(X) and Dim−(X) whose reduction modulo p is the categorical dimension dim(X) of X, coinciding with the usual dimension when X is a vector space. We study properties of Dim±(X), and in particular show that they don’t always coincide with each other, and can take any value in Z [subscript]p. We also discuss the connection of p-adic dimensions with the theory of λ-rings and Brauer characters. ©2018 Keywords: tensor categories; symmetric monoidal categories |
| first_indexed | 2024-09-23T11:13:10Z |
| format | Article |
| id | mit-1721.1/124324 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:13:10Z |
| publishDate | 2020 |
| publisher | European Mathematical Publishing House |
| record_format | dspace |
| spelling | mit-1721.1/1243242022-09-27T17:57:05Z p-adic dimensions in symmetric tensor categories in characteristic p Etingof, Pavel I Harman, Nate Ostrik, Victor Massachusetts Institute of Technology. Department of Mathematics To every object X of a symmetric tensor category over a field of characteristic p > 0 we attach p-adic integers Dim+(X) and Dim−(X) whose reduction modulo p is the categorical dimension dim(X) of X, coinciding with the usual dimension when X is a vector space. We study properties of Dim±(X), and in particular show that they don’t always coincide with each other, and can take any value in Z [subscript]p. We also discuss the connection of p-adic dimensions with the theory of λ-rings and Brauer characters. ©2018 Keywords: tensor categories; symmetric monoidal categories NSF (Grant DMS-1502244) National Science Foundation Graduate Research Fellowship (Grant no. 1122374) 2020-03-25T17:26:53Z 2020-03-25T17:26:53Z 2018-02 2019-11-12T17:30:31Z Article http://purl.org/eprint/type/JournalArticle 1664-073X 1663-487X https://hdl.handle.net/1721.1/124324 Etingof, Pavel, Nate Harman, and Victor Ostrik, "p-adic dimensions in symmetric tensor categories in characteristic p." Quantum topology 9, 1 (Feb. 2018): p. 119-40 doi:: 10.4171/QT/104 ©2018 Author(s) en 10.4171/QT/104 Quantum topology Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf European Mathematical Publishing House arXiv |
| spellingShingle | Etingof, Pavel I Harman, Nate Ostrik, Victor p-adic dimensions in symmetric tensor categories in characteristic p |
| title | p-adic dimensions in symmetric tensor categories in characteristic p |
| title_full | p-adic dimensions in symmetric tensor categories in characteristic p |
| title_fullStr | p-adic dimensions in symmetric tensor categories in characteristic p |
| title_full_unstemmed | p-adic dimensions in symmetric tensor categories in characteristic p |
| title_short | p-adic dimensions in symmetric tensor categories in characteristic p |
| title_sort | p adic dimensions in symmetric tensor categories in characteristic p |
| url | https://hdl.handle.net/1721.1/124324 |
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