Communications in Mathematical Physics

, Volume 279, Issue 1, pp 77–116

The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere

  • Francesco D’Andrea
  • Ludwik Da̧browski
  • Giovanni Landi
Article

DOI: 10.1007/s00220-008-0420-x

Cite this article as:
D’Andrea, F., Da̧browski, L. & Landi, G. Commun. Math. Phys. (2008) 279: 77. doi:10.1007/s00220-008-0420-x

Abstract

Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere \(S^4_q\). These representations are the constituents of a spectral triple on \(S^4_q\) with a Dirac operator which is isospectral to the canonical one on the round sphere S4 and which then gives 4+-summability. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an ‘instanton’ projection. We also introduce a real structure which satisfies all required properties modulo smoothing operators.

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Francesco D’Andrea
    • 1
  • Ludwik Da̧browski
    • 1
  • Giovanni Landi
    • 2
    • 3
  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità di TriesteTriesteItaly
  3. 3.INFN, Sezione di TriesteTriesteItaly