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Deformed noncommutative tori
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-8727-2169
Mathematical Physics, Austria .
2012 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 53, no 7, 073505- p.Article in journal (Refereed) Published
Abstract [en]

We recall a construction of non-commutative algebras related to a one-parameter family of (deformed) spheres and tori, and show that in the case of tori, the *-algebras can be completed into C*-algebras isomorphic to the standard non-commutative torus. As the former was constructed in the context of matrix (or fuzzy) geometries, it provides an important link to the framework of non-commutative geometry, and opens up for a concrete way to study deformations of non-commutative tori. Furthermore, we show how the well-known fuzzy sphere and fuzzy torus can be obtained as formal scaling limits of finite-dimensional representations of the deformed algebras, and their projective modules are described together with connections of constant curvature.

Place, publisher, year, edition, pages
American Institute of Physics (AIP) , 2012. Vol. 53, no 7, 073505- p.
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-82075DOI: 10.1063/1.4732099ISI: 000307609900030OAI: diva2:557696
Available from: 2012-09-28 Created: 2012-09-28 Last updated: 2013-08-29

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Arnlind, Joakim
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