Dirac Operators on Quantum Projective Spaces |
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Authors: | Francesco D’Andrea Ludwik D?browski |
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Institution: | (1) Institute of Mathematical Sciences, CIT Campus, Chennai, 600 113, India;(2) Indian Statistical Institute, 7, SJSS Marg, New Delhi, 110 016, India |
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Abstract: | We construct a family of self-adjoint operators D N , ${N\in{\mathbb Z}}We construct a family of self-adjoint operators D
N
,
N ? \mathbb Z{N\in{\mathbb Z}} , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space
\mathbb CPlq{{\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=\frac12(l+1){N=\frac{1}{2}(\ell+1)} , the spectral triple is real with KO-dimension 2ℓ mod 8. |
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Keywords: | |
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