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Entwining Yang-Baxter maps and integrable lattices

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Kouloukas T., Papageorgiou V.

Banach Center Publications

2011

tom 93

nr 1

163-175

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 L₁, L₂, L₃ derived from symplectic leaves of 2 × 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 L₁ = L₂ = L₃ 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.

Ograniczanie wyników

1 Banach Center Publications

1 Kouloukas T.

1 Papageorgiou V.

1 2011

Wyniki wyszukiwania

Entwining Yang-Baxter maps and integrable lattices