The Podleś sphere as a spectral metric space

Konrad Aguilar, Jens Kaad*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We study the spectral metric aspects of the standard Podleś sphere, which is a homogeneous space for quantum SU(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.

Original languageEnglish
JournalJournal of Geometry and Physics
Volume133
Pages (from-to)260-278
ISSN0393-0440
DOIs
Publication statusPublished - Nov 2018

Keywords

  • Lip-norms
  • Podleś sphere
  • Quantum metric spaces
  • Spectral triples

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