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

In: Physical and Mathematical Aspects of Symmetries

Author

Listed:
  • Hendrik De Bie

    (Ghent University, Department of Mathematical Analysis, Faculty of Engineering and Architecture)

  • Vincent X. Genest

    (Masschusetts Institute of Technology, Department of Mathematics)

  • Wouter van de Vijver

    (Ghent University, Department of Mathematical Analysis, Faculty of Engineering and Architecture)

  • Luc Vinet

    (Université de Montréal, Centre de Recherches Mathématiques)

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.

Suggested Citation

  • Hendrik De Bie & Vincent X. Genest & Wouter van de Vijver & Luc Vinet, 2017. "Bannai–Ito algebras and the osp(1;2) superalgebra," Springer Books, in: Sergio Duarte & Jean-Pierre Gazeau & Sofiane Faci & Tobias Micklitz & Ricardo Scherer & Francesco To (ed.), Physical and Mathematical Aspects of Symmetries, pages 349-354, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-69164-0_52
    DOI: 10.1007/978-3-319-69164-0_52
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