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Quantum Differentiability on Quantum Tori

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, UNSW, Kensington, NSW, 2052, Australia

    Edward Mcdonald, Fedor Sukochev & Xiao Xiong

  2. Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Xiao Xiong

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  1. Edward Mcdonald
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  2. Fedor Sukochev
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  3. Xiao Xiong
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Correspondence to Edward Mcdonald.

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Communicated by Y. Kawahigashi

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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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