Abstract
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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Acknowledgements
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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Mcdonald, E., Sukochev, F. & Xiong, X. Quantum Differentiability on Quantum Tori. Commun. Math. Phys. 371, 1231–1260 (2019). https://doi.org/10.1007/s00220-019-03384-w
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DOI: https://doi.org/10.1007/s00220-019-03384-w