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Classical r-matrices of two- and three-dimensional Lie superbialgebras and their Poisson-Lie supergroups

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Abstract

We obtain the classical r-matrices of two- and three-dimensional Lie superbialgebras. We thus classify all two- and three-dimensional coboundary Lie superbialgebras and their types (triangular, quasitriangular, or factorable). Using the Sklyanin superbracket, we then obtain the super Poisson structures on the related Poisson-Lie supergroups.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, Azarbaijan Shahid Madani University, Tabriz, Iran

    A. Eghbali & A. Rezaei-Aghdam

Authors
  1. A. Eghbali
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  2. A. Rezaei-Aghdam
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Correspondence to A. Rezaei-Aghdam.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 172, No. 1, pp. 100–121, July, 2012.

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Eghbali, A., Rezaei-Aghdam, A. Classical r-matrices of two- and three-dimensional Lie superbialgebras and their Poisson-Lie supergroups. Theor Math Phys 172, 963–986 (2012). https://doi.org/10.1007/s11232-012-0089-3

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  • DOI: https://doi.org/10.1007/s11232-012-0089-3

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