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Physical and Mathematical Aspects of Symmetries pp 349–354Cite as

Bannai–Ito algebras and the osp(1;2) superalgebra

Abstract

The Bannai–Ito algebra B(n) of rank (n – 2) is defined as the algebra generated by the Casimir operators arising in the n-fold tensor product of the osp(1,2) superalgebra. The structure relations are presented and representations in bases determined by maximal Abelian subalgebras are discussed. Comments on realizations as symmetry algebras of physical models are offered.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Engineering and Architecture, Ghent University, Ghent, Belgium

    Hendrik De Bie & Wouter van de Vijver

  2. Department of Mathematics, Masschusetts Institute of Technology, Cambridge, USA

    Vincent X. Genest

  3. Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada

    Luc Vinet

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

Correspondence to Hendrik De Bie .

Editor information

Editors and Affiliations

  1. Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro, Brazil

    Ph.D. Sergio Duarte

  2. Laboratoire APC, Paris Diderot University, Paris, France

    Prof. Jean-Pierre Gazeau

  3. Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro, Brazil

    Sofiane Faci

  4. Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro, Brazil

    Tobias Micklitz

  5. Universidade Federal Rural do Rio de Janeiro, Seropédica, Rio de Janeiro, Brazil

    Ricardo Scherer

  6. Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro, Brazil

    Francesco Toppan

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De Bie, H., Genest, V.X., van de Vijver, W., Vinet, L. (2017). Bannai–Ito algebras and the osp(1;2) superalgebra. In: Duarte, S., Gazeau, JP., Faci, S., Micklitz, T., Scherer, R., Toppan, F. (eds) Physical and Mathematical Aspects of Symmetries. Springer, Cham. https://doi.org/10.1007/978-3-319-69164-0_52

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