Real spectral triples over noncommutative Bieberbach manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:73

Article

Olczykowski, Piotr¹  Sitarz, Andrzej^2,3 

[1] Copernicus Ctr Interdisciplinary Studies, PL-31016 Krakow, Poland

[2] Jagiellonian Univ, Inst Phys, PL-30059 Krakow, Poland

[3] Polish Acad Sci, Inst Math, PL-00950 Warsaw, Poland

关键词: Noncommutative geometry;    Spectral triple;    Dirac operator;   

DOI  :  10.1016/j.geomphys.2013.05.003

来源: Elsevier

【 摘 要 】

We classify and construct all real spectral triples over noncommutative Bieberbach manifolds, which are restrictions of irreducible, real, equivariant spectral triples over the noncommutative three-torus. We show that, in the classical case, the constructed geometries correspond exactly to spin structures over Bieberbach manifolds and the Dirac operators constructed for a flat metric. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free