An Asymmetric Noncommutative Torus

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Authors: Dąbrowski, L., Sitarz, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147144
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: An Asymmetric Noncommutative Torus / L. Dąbrowski, A. Sitarz // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 16 назв. — англ.

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 no...