Communications in Mathematical Physics

, Volume 279, Issue 1, pp 77–116

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


    • Scuola Internazionale Superiore di Studi Avanzati
  • Ludwik Da̧browski
    • Scuola Internazionale Superiore di Studi Avanzati
  • Giovanni Landi
    • Dipartimento di Matematica e InformaticaUniversità di Trieste
    • INFN, Sezione di Trieste

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


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.

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© Springer-Verlag 2008