The Podles spheres converge to the sphere

Abstract

We prove that the Podles spheres $S_q^2$ converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter $q$ tends to 1. Moreover, we construct a $q$-deformed analogue of the fuzzy spheres, and prove that they converge to $S_q^2$ as their linear dimension tends to infinity, thus providing a quantum counterpart to a classical result of Rieffel.

arXiv comment34 pages

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Cited by in corpus (1)

• Convergence of Fourier truncations for compact quantum groups and finitely generated groups