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Generalized Fuzzy Torus and its Modular Properties
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2013_9_a59,
     author = {Paul Schreivogl and Harold Steinacker},
     title = {Generalized {Fuzzy} {Torus} and its {Modular} {Properties}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     volume = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a59/}
}
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Paul Schreivogl; Harold Steinacker. Generalized Fuzzy Torus and its Modular Properties. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a59/

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