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: Schreivogl, P., Steinacker, H.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2013
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
id nasplib_isofts_kiev_ua-123456789-149352
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Generalized Fuzzy Torus and its Modular Properties
spellingShingle Generalized Fuzzy Torus and its Modular Properties
Schreivogl, P.
Steinacker, H.
title_short 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_sort generalized fuzzy torus and its modular properties
author Schreivogl, P.
Steinacker, H.
author_facet Schreivogl, P.
Steinacker, H.
publishDate 2013
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149352
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.
work_keys_str_mv AT schreivoglp generalizedfuzzytorusanditsmodularproperties
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first_indexed 2025-12-07T17:56:46Z
last_indexed 2025-12-07T17:56:46Z
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