The Podleś sphere as a spectral metric space

Abstract

We study the spectral metric aspects of the standard Podleś sphere, which is a homogeneous space for quantum S U ( 2 ) . The point of departure is the real equivariant spectral triple investigated by Dąbrowski and Sitarz. The Dirac operator of this spectral triple interprets the standard Podleś 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 Podleś sphere with the structure of a compact quantum metric space in the sense of Rieffel.