Entwining Yang-Baxter maps and integrable lattices

• Autorzy: Theodoros E. Kouloukas , Vassilios G. Papageorgiou
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 17B80: Applications to integrable systems
• 17B63: Poisson algebras
• 81R50: Quantum groups and related algebraic methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 93
• Numer: 1
• Strony: 163-175

Daty

wydano

2011

Twórcy

autor

Theodoros E. Kouloukas

• Department of Mathematics, University of Patras, GR-265 00 Patras, Greece

autor

Vassilios G. Papageorgiou

• Department of Mathematics, University of Patras, GR-265 00 Patras, Greece

Identyfikatory

DOI

10.4064/bc93-0-13