The Podles sphere as a spectral metric space
arXiv:1803.03027 · doi:10.1016/j.geomphys.2018.07.015
Abstract
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.
24 pages
References in corpus (1)
Cited by in corpus (4)
- The Podles spheres converge to the sphere
- Convergence of Fourier truncations for compact quantum groups and finitely generated groups
- Continuity of the Spectrum of Dirac Operators of Spectral Triples for the Spectral Propinquity
- Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum Tori