Classification of homogeneous Fourier matrices
Modular data are commonly studied in mathematics and physics. A modular datum defines a finite-dimensional representation of the modular group \(SL_2(\mathbb{Z})\). In this paper, we show that there is a one-to-one correspondence between Fourier matrices associated to modular data and self-dual \(C...
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| Date: | 2019 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2019
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/446 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543306463313920 |
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| author | Singh, Gurmail |
| author_facet | Singh, Gurmail |
| author_sort | Singh, Gurmail |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2019-04-09T04:51:45Z |
| description | Modular data are commonly studied in mathematics and physics. A modular datum defines a finite-dimensional representation of the modular group \(SL_2(\mathbb{Z})\). In this paper, we show that there is a one-to-one correspondence between Fourier matrices associated to modular data and self-dual \(C\)-algebras that satisfy a certain condition. We prove that a homogenous \(C\)-algebra arising from a Fourier matrix has all the degrees equal to \(1\). |
| first_indexed | 2025-12-02T15:26:47Z |
| format | Article |
| id | admjournalluguniveduua-article-446 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:26:47Z |
| publishDate | 2019 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-4462019-04-09T04:51:45Z Classification of homogeneous Fourier matrices Singh, Gurmail modular data, Fourier matrices, fusion rings, \(C\)-algebras 05E30; 05E99; 81R05 Modular data are commonly studied in mathematics and physics. A modular datum defines a finite-dimensional representation of the modular group \(SL_2(\mathbb{Z})\). In this paper, we show that there is a one-to-one correspondence between Fourier matrices associated to modular data and self-dual \(C\)-algebras that satisfy a certain condition. We prove that a homogenous \(C\)-algebra arising from a Fourier matrix has all the degrees equal to \(1\). Lugansk National Taras Shevchenko University 2019-03-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/446 Algebra and Discrete Mathematics; Vol 27, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/446/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/446/193 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/446/504 Copyright (c) 2019 Algebra and Discrete Mathematics |
| spellingShingle | modular data Fourier matrices fusion rings \(C\)-algebras 05E30 05E99 81R05 Singh, Gurmail Classification of homogeneous Fourier matrices |
| title | Classification of homogeneous Fourier matrices |
| title_full | Classification of homogeneous Fourier matrices |
| title_fullStr | Classification of homogeneous Fourier matrices |
| title_full_unstemmed | Classification of homogeneous Fourier matrices |
| title_short | Classification of homogeneous Fourier matrices |
| title_sort | classification of homogeneous fourier matrices |
| topic | modular data Fourier matrices fusion rings \(C\)-algebras 05E30 05E99 81R05 |
| topic_facet | modular data Fourier matrices fusion rings \(C\)-algebras 05E30 05E99 81R05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/446 |
| work_keys_str_mv | AT singhgurmail classificationofhomogeneousfouriermatrices |