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