Deformed Noncommutative Tori
Abstract
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.
Keywords
Cite
@article{arxiv.1201.2754,
title = {Deformed Noncommutative Tori},
author = {Joakim Arnlind and Harald Grosse},
journal= {arXiv preprint arXiv:1201.2754},
year = {2015}
}