We prove that the Podleś spheres S2q 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 S2q as their linear dimension tends to infinity, thus providing a quantum counterpart to a classical result of Rieffel.
|Journal||Communications in Mathematical Physics|
|Publication status||Published - Jun 2022|
Bibliographical noteFunding Information:
The authors gratefully acknowledge the financial support from the Independent Research Fund Denmark through Grant Nos. 9040-00107B and 7014-00145B. Furthermore, they would like to thank Marc Rieffel for pointing out the reference , and the anonymous referees for their careful reading of the manuscript.
- 58B32, 58B34, 46L89, 46L30, 81R15, 81R60