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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 060, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.060
(Mi sigma843)
 

This article is cited in 7 scientific papers (total in 7 papers)

Generalized Fuzzy Torus and its Modular Properties

Paul Schreivogl, Harold Steinacker

Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
Full-text PDF (533 kB) Citations (7)
References:
Abstract: 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 $\tau$. 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.
Keywords: fuzzy spaces; noncommutative geometry; matrix models.
Received: June 19, 2013; in final form October 11, 2013; Published online October 17, 2013
Bibliographic databases:
Document Type: Article
MSC: 81R60; 81T75; 81T30
Language: English
Citation: Paul Schreivogl, Harold Steinacker, “Generalized Fuzzy Torus and its Modular Properties”, SIGMA, 9 (2013), 060, 23 pp.
Citation in format AMSBIB
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\by Paul~Schreivogl, Harold~Steinacker
\paper Generalized Fuzzy Torus and its Modular Properties
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\yr 2013
\vol 9
\papernumber 060
\totalpages 23
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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