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Entwining Yang-Baxter maps and integrable lattices

Tom 93 / 2011

Theodoros E. Kouloukas, Vassilios G. Papageorgiou Banach Center Publications 93 (2011), 163-175 MSC: Primary 81R50; Secondary 17B80, 17B63. DOI: 10.4064/bc93-0-13

Streszczenie

Yang–Baxter (YB) map systems (or set-theoretic analogs of entwining YB structures) are presented. They admit zero curvature representations with spectral parameter depended Lax triples $L_1,\ L_2,\ L_3$ derived from symplectic leaves of $2 \times 2$ binomial matrices equipped with the Sklyanin bracket. A unique factorization condition of the Lax triple implies a 3-dimensional compatibility property of these maps. In case $L_1=L_2=L_3$ this property yields the set-theoretic quantum Yang-Baxter equation, i.e. the YB map property. By considering periodic `staircase' initial value problems on quadrilateral lattices, these maps give rise to multidimensional integrable mappings which preserve the spectrum of the corresponding monodromy matrix.

Autorzy

  • Theodoros E. KouloukasDepartment of Mathematics
    University of Patras
    GR-265 00 Patras, Greece
    e-mail
  • Vassilios G. PapageorgiouDepartment of Mathematics
    University of Patras
    GR-265 00 Patras, Greece
    e-mail

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