On twisted reality conditions

Abstract

We study the twisted reality condition of Brzeziński et al. (Math Phys Anal Geom 19(3):11, 2016), for spectral triples, in particular with respect to the product and the commutant. Motivated by this, we present the procedure, which allows one to untwist the twisted spectral triples studied in Landi and Martinetti (Lett Math Phys 106:1499–1530, 2016). We also relate this construction to conformally rescaled real twisted spectral triples and discuss the untwisting of the “minimal twist” procedure of an even spectral triple.

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Acknowledgements

The authors would like to thank for hospitality the Institute of Mathematics of Polish Academy of Sciences (IMPAN), where the work on the present note started. Likewise, the first two authors are grateful for the hospitality of the Faculty of Physics, Astronomy and Applied Computer Science of the Jagiellonian University in Kraków, where the work was completed. The research of all authors is partially supported by the Polish National Science Centre Grant 2016/21/B/ST1/02438.

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Correspondence to Tomasz Brzeziński.

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Brzeziński, T., Dąbrowski, L. & Sitarz, A. On twisted reality conditions. Lett Math Phys 109, 643–659 (2019). https://doi.org/10.1007/s11005-018-1120-x

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Keywords

  • Spectral triple
  • Twisted spectral triple
  • Twisted reality conditions
  • Minimal twist

Mathematics Subject Classification

  • 58B34
  • 58B32
  • 46L87