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Quantum Theory and Symmetries pp 209–216Cite as

The Racah Algebra and

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Part of the CRM Series in Mathematical Physics book series (CRM)

Abstract

We conjecture the existence of an embedding of the Racah algebra into the universal enveloping algebra of . Evidence of this conjecture is offered by realizing both algebras using differential operators and giving an embedding in this realization.

Keywords

  • Racah algebra
  • Embedding
  • Lie algebra

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  • DOI: 10.1007/978-3-030-55777-5_19
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Acknowledgements

The work of HDB is supported by the Research Foundation Flanders (FWO) under Grant EOS 30889451. HDB and WVDV are grateful for the hospitality extended to them by the Centre de Recherches Mathématiques in Montréal, where part of this research was carried out. The research of LV is funded in part by a discovery grant of the Natural Sciences and Engineering Council (NSERC) of Canada.

Author information

Authors and Affiliations

  1. Department of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University, Gent, Belgium

    Hendrik De Bie & Wouter van de Vijver

  2. Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada

    Luc Vinet

Authors
  1. Hendrik De Bie
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  2. Luc Vinet
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  3. Wouter van de Vijver
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Corresponding author

Correspondence to Hendrik De Bie .

Editor information

Editors and Affiliations

  1. Département de physique, Université de Montréal, Montréal, QC, Canada

    Prof. M. B. Paranjape

  2. Département de physique, Université de Montréal, Montréal, QC, Canada

    Prof. Richard MacKenzie

  3. Department of Mathematics and Physics, SUNY Polytechnic Institute, Utica, NY, USA

    Prof. Zora Thomova

  4. Department of Mathematics and Statistics, Université de Montréal, Montréal, QC, Canada

    Prof. Pavel Winternitz

  5. Département de physique, Université de Montréal, Montréal, QC, Canada

    Prof. William Witczak-Krempa

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Bie, H.D., Vinet, L., van de Vijver, W. (2021). The Racah Algebra and . In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P., Witczak-Krempa, W. (eds) Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-55777-5_19

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