Abstract
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.
Original language | English |
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Journal | Communications in Mathematical Physics |
Volume | 392 |
Issue number | 3 |
Pages (from-to) | 1029-1061 |
ISSN | 0010-3616 |
DOIs | |
Publication status | Published - Jun 2022 |
Bibliographical note
Funding 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.
Keywords
- math.OA
- math.FA
- 58B32, 58B34, 46L89, 46L30, 81R15, 81R60