Generalized Fuzzy Torus and its Modular Properties
We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149352 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Generalized Fuzzy Torus and its Modular Properties / P. Schreivogl, H. Steinacker // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715219236618240 |
|---|---|
| author | Schreivogl, P. Steinacker, H. |
| author_facet | Schreivogl, P. Steinacker, H. |
| citation_txt | Generalized Fuzzy Torus and its Modular Properties / P. Schreivogl, H. Steinacker // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter τ. The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operator is also computed.
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| first_indexed | 2025-12-07T17:56:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149352 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:56:46Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Schreivogl, P. Steinacker, H. 2019-02-21T07:09:00Z 2019-02-21T07:09:00Z 2013 Generalized Fuzzy Torus and its Modular Properties / P. Schreivogl, H. Steinacker // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R60; 81T75; 81T30 DOI: http://dx.doi.org/10.3842/SIGMA.2013.060 https://nasplib.isofts.kiev.ua/handle/123456789/149352 We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter τ. The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operator is also computed. This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
 full collection is available at http://www.emis.de/journals/SIGMA/space-time.html.
 This work was supported by the Austrian Science Fund (FWF) under the contracts P21610 and
 P24713. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Generalized Fuzzy Torus and its Modular Properties Article published earlier |
| spellingShingle | Generalized Fuzzy Torus and its Modular Properties Schreivogl, P. Steinacker, H. |
| title | Generalized Fuzzy Torus and its Modular Properties |
| title_full | Generalized Fuzzy Torus and its Modular Properties |
| title_fullStr | Generalized Fuzzy Torus and its Modular Properties |
| title_full_unstemmed | Generalized Fuzzy Torus and its Modular Properties |
| title_short | Generalized Fuzzy Torus and its Modular Properties |
| title_sort | generalized fuzzy torus and its modular properties |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149352 |
| work_keys_str_mv | AT schreivoglp generalizedfuzzytorusanditsmodularproperties AT steinackerh generalizedfuzzytorusanditsmodularproperties |