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Quantum even spheres Sigma_q^2n from Poisson double suspension

F. Bonechi·N. Ciccoli·M. Tarlini
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Abstract

We define even dimensional quantum spheres Sigma_q^2n that generalize to higher dimension the standard quantum two-sphere of Podle's and the four-sphere Sigma_q^4 obtained in the quantization of the Hopf bundle. The construction relies on an iterated Poisson double suspension of the standard Podle's two-sphere. The Poisson spheres that we get have the same symplectic foliation consisting of a degenerate point and a symplectic plane and, after quantization, have the same C^*-algebraic completion. We investigate their K-homology and K-theory by introducing Fredholm modules and projectors.

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F. Bonechi, N. Ciccoli, M. Tarlini. 2002-11-29. Quantum even spheres Sigma_q^2n from Poisson double suspension. https://doi.org/10.1007/s00220-003-0971-9

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