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On twisted reality conditions

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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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Authors and Affiliations

  1. Department of Mathematics, Swansea University, Swansea, SA2 8PP, UK

    Tomasz Brzeziński

  2. Department of Mathematics, University of Białystok, K. Ciołkowskiego 1M, 15-245, Białystok, Poland

    Tomasz Brzeziński

  3. SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136, Trieste, Italy

    Ludwik Dąbrowski

  4. Institute of Physics, Jagiellonian University, Prof. Stanisława Łojasiewicza 11, 30-348, Kraków, Poland

    Andrzej Sitarz

  5. Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-950, Warszawa, Poland

    Andrzej Sitarz

Authors
  1. Tomasz Brzeziński
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  2. Ludwik Dąbrowski
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  3. Andrzej Sitarz
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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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  • DOI: https://doi.org/10.1007/s11005-018-1120-x

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