Deformed noncommutative tori
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
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.
IdentifiersURN: urn:nbn:se:liu:diva-82075DOI: 10.1063/1.4732099ISI: 000307609900030OAI: oai:DiVA.org:liu-82075DiVA: diva2:557696