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Deformed noncommutative tori

Autor(en)
Joakim Arnlind, Harald Grosse
Abstrakt

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.

Organisation(en)
Mathematische Physik
Externe Organisation(en)
Linköping University
Journal
Journal of Mathematical Physics
Band
53
Anzahl der Seiten
9
ISSN
0022-2488
DOI
https://doi.org/10.1063/1.4732099
Publikationsdatum
2012
Peer-reviewed
Ja
ÖFOS 2012
103019 Mathematische Physik
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/133902d7-59cd-4052-a93d-651881d7f6a4