Communications in Mathematical Physics

, Volume 295, Issue 3, pp 731–790

Dirac Operators on Quantum Projective Spaces


DOI: 10.1007/s00220-010-0989-8

Cite this article as:
D’Andrea, F. & Dąbrowski, L. Commun. Math. Phys. (2010) 295: 731. doi:10.1007/s00220-010-0989-8


We construct a family of self-adjoint operators DN, \({N\in{\mathbb Z}}\) , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space \({{\mathbb C}{\rm P}^{\ell}_q}\) , for any  ≥ 2 and 0 < q < 1. They provide 0+-dimensional equivariant even spectral triples. If is odd and \({N=\frac{1}{2}(\ell+1)}\) , the spectral triple is real with KO-dimension 2 mod 8.

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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Dép. de MathématiqueU.C. LouvainLouvain-La-NeuveBelgique
  2. 2.Scuola Internazionale Superiore di Studi AvanzatiTriesteItalia