Communications in Mathematical Physics

, Volume 371, Issue 3, pp 1231–1260 | Cite as

Quantum Differentiability on Quantum Tori

  • Edward McdonaldEmail author
  • Fedor Sukochev
  • Xiao Xiong


We provide a full characterisation of quantum differentiability (in the sense of Connes) on quantum tori. We also prove a quantum integration formula which differs substantially from the commutative case.


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The authors wish to thank the anonymous referees for careful reading and useful sugges tions; in particular one referee pointed out how our main results could be proved without an L∞ condition.We are also greatly indebted to Professor Raphaël Ponge for many helpful comments on the section of Pseudodif ferential Operators. The authors are supported by Australian Research Council (Grant No. FL170100052); X. Xiong is also partially supported by the National Natural Science Foundation of China (Grant No. 11301401).


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUNSWKensingtonAustralia
  2. 2.Institute for Advanced Study in MathematicsHarbin Institute of TechnologyHarbinChina

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