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Jordanian quantum deformations of D = 4 anti-de Sitter and Poincaré superalgebras

  • theoretical physics
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Abstract.

We consider a superextension of the extended Jordanian twist, describing the non-standard quantization of the anti-de Sitter (AdS) superalgebra \(\mathfrak {osp}(1\vert 4)\) in the form of a Hopf superalgebra. The super-Jordanian twisting function and corresponding basic coproduct formulae for the generators of \(\mathfrak {osp}(1\vert 4)\) are given in explicit form. A non-linear transformation of the classical superalgebra basis not modifying the defining algebraic relations but simplifying coproducts and antipodes is proposed. Our physical application is in the interpretation of the new super-Jordanian deformation of the \(\mathfrak {osp}(1\vert 4)\) superalgebra as deformed D = 4 AdS supersymmetries. Subsequently we perform a suitable contraction of the quantum Jordanian AdS superalgebra and obtain a new \(\kappa\)-deformation of the D = 4 Poincaré superalgebra, with the bosonic sector describing the light-cone \(\kappa\)-deformation of the Poincaré symmetries.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Wrocław, pl. Maxa Borna 9, 50-205, Wrocław, Poland

    A. Borowiec, J. Lukierski & V. N. Tolstoy

  2. Institute of Nuclear Physics, Moscow State University, 119 992, Moscow, Russia

    V. N. Tolstoy

Authors
  1. A. Borowiec
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  2. J. Lukierski
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  3. V. N. Tolstoy
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Correspondence to J. Lukierski.

Additional information

Received: 19 December 2004, Revised: 13 June 2005, Published online: 19 August 2005

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Borowiec, A., Lukierski, J. & Tolstoy, V.N. Jordanian quantum deformations of D = 4 anti-de Sitter and Poincaré superalgebras. Eur. Phys. J. C 44, 139–145 (2005). https://doi.org/10.1140/epjc/s2005-02338-2

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