The Podles sphere as a spectral metric space

JOURNAL OF GEOMETRY AND PHYSICS

卷:133

Article

Aguilar, Konrad¹  Kaad, Jens² 

[1] Arizona State Univ, Sch Math & Stat Sci, 901 S Palm Walk, Tempe, AZ 85287 USA

[2] Univ Southern Denmark, Dept Math & Comp Sci, Campusvej 55, DK-5230 Odense M, Denmark

关键词: Quantum metric spaces;    Lip-norms;    Podles sphere;    Spectral triples;   

DOI  :  10.1016/j.geomphys.2018.07.015

来源: Elsevier

【 摘 要 】

We study the spectral metric aspects of the standard Podles sphere, which is a homogeneous space for quantum SU(2). The point of departure is the real equivariant spectral triple investigated by Dabrowski and Sitarz. The Dirac operator of this spectral triple interprets the standard Podles sphere as a 0-dimensional space and is therefore not isospectral to the Dirac operator on the 2-sphere. We show that the seminorm coming from commutators with this Dirac operator provides the Podles sphere with the structure of a compact quantum metric space in the sense of Rieffel. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free