The Podles sphere as a spectral metric space

被引：17

作者：

Aguilar, Konrad ^{[1
]}

Kaad, Jens ^{[2
]}

机构：

[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

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2018年 / 133卷

基金：

欧盟地平线“2020”;

关键词：

Quantum metric spaces; Lip-norms; Podles sphere; Spectral triples; QUANTUM SPHERES; ALGEBRAS; FORMULA;

D O I：

10.1016/j.geomphys.2018.07.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：260 / 278

页数：19