An Asymmetric Noncommutative Torus

Symmetry Integrability and Geometry-Methods and Applications

article

Ludwik Dąbrowski¹  Andrzej Sitarz² 

[1] SISSA (Scuola Internazionale Superiore di Studi Avanzati);Institute of Physics, Jagiellonian University, Poland Institute of Physics, Jagiellonian University

关键词: noncommutative geometry;    Gauss–Bonnet;    spectral triple;   

DOI  :  10.3842/SIGMA.2015.075

来源: National Academy of Science of Ukraine

【 摘 要 】

We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the dressed scalar curvature and show that the Gauss-Bonnet theorem holds (which is not covered by the general result of Connes and Moscovici).

【 授权许可】

Unknown