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Abstract: Yang-Baxter YB map systems or set-theoretic analoga of entwining YBstructures are presented. They admit zero curvature representations withspectral parameter depended Lax triples L1, L2, L3 derived from symplecticleaves of 2 x 2 binomial matrices equipped with the Sklyanin bracket. A uniquefactorization condition of the Lax triple implies a 3-dimensional compatibilityproperty of these maps. In case L1 = L2 = L3 this property yields these-theoretic quantum Yang-Baxter equation, i.e. the YB map property. Byconsidering periodic -staircase- initial value problems on quadrilaterallattices, these maps give rise to multidimensional integrable mappings whichpreserve the spectrum of the corresponding monodromy matrix.

Autor: Theodoros E. Kouloukas, Vassilios G. Papageorgiou

Fuente: https://arxiv.org/

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