Abstract
We construct a family of self-adjoint operators D N , \({N\in{\mathbb Z}}\) , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space \({{\mathbb C}{\rm P}^{\ell}_q}\) , for any ℓ ≥ 2 and 0 < q < 1. They provide 0+-dimensional equivariant even spectral triples. If ℓ is odd and \({N=\frac{1}{2}(\ell+1)}\) , the spectral triple is real with KO-dimension 2ℓ mod 8.
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Communicated by A. Connes
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D’Andrea, F., Dąbrowski, L. Dirac Operators on Quantum Projective Spaces. Commun. Math. Phys. 295, 731–790 (2010). https://doi.org/10.1007/s00220-010-0989-8
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DOI: https://doi.org/10.1007/s00220-010-0989-8