Entwining Yang-Baxter maps and integrable lattices

Theodoros E. Kouloukas, and Vassilios G. Papageorgiou. "Entwining Yang-Baxter maps and integrable lattices." Banach Center Publications 93.1 (2011): 163-175. <http://eudml.org/doc/281958>.

@article{TheodorosE2011,
abstract = {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.},
author = {Theodoros E. Kouloukas, Vassilios G. Papageorgiou},
journal = {Banach Center Publications},
keywords = {Yang-Baxter map; three-dimensional compatibility; entwining Yang-Baxter structures},
language = {eng},
number = {1},
pages = {163-175},
title = {Entwining Yang-Baxter maps and integrable lattices},
url = {http://eudml.org/doc/281958},
volume = {93},
year = {2011},
}

TY - JOUR
AU - Theodoros E. Kouloukas
AU - Vassilios G. Papageorgiou
TI - Entwining Yang-Baxter maps and integrable lattices
JO - Banach Center Publications
PY - 2011
VL - 93
IS - 1
SP - 163
EP - 175
AB - 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.
LA - eng
KW - Yang-Baxter map; three-dimensional compatibility; entwining Yang-Baxter structures
UR - http://eudml.org/doc/281958
ER -