Spin geometry of the rational noncommutative torus

JOURNAL OF GEOMETRY AND PHYSICS

卷:144

Article

Carotenuto, Alessandro¹  Dabrowski, Ludwik¹ 

[1] SISSA, Via Bonomea 265, I-34136 Trieste, Italy

关键词: Noncommutative torus;    Spectral triples;    Conformal perturbations;    Spin structures;   

DOI  :  10.1016/j.geomphys.2019.05.008

来源: Elsevier

【 摘 要 】

We discuss the structure of topologically non-trivial almost-commutative manifold for spectral triples realized on the algebra of smooth functions on the noncommutative torus with rational parameter. This is done by showing isomorphisms with a spectral triple on the algebra of sections of certain bundle of algebras, and with a spectral triple on a certain invariant subalgebra of the product algebra. The isomorphisms intertwine also the grading and real structure. This holds for all four inequivalent spin structures, which are explicitly constructed in terms of double coverings of the noncommutative torus (with arbitrary real parameter). These results are extended also to a class of curved (non flat) spectral triples, obtained as a perturbation of the standard one by eight central elements. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free