2002/05/31 by A. P. Veselov · 3 citations
Mathematics · #math.QA #math.DS #msc:81R12
paper · pdf · doi:10.1016/s0375-9601(03)00915-0
Revised version based on the talks at NEEDS conference (Cadiz, 10-15 June 2002) and SIDE-V conference (Giens, 21-26 June 2002)
arxiv created 2002/07/05 · arxiv updated 2009/11/30
The hierarchy of commuting maps related to a set-theoretical solution of the quantum Yang-Baxter equation (Yang-Baxter map) is introduced. They can be considered as dynamical analogues of the monodromy and/or transfer-matrices. The general scheme of producing Yang-Baxter maps based on matrix factorisation is discussed in the context of the integrability problem for the corresponding dynamical systems. Some examples of birational Yang-Baxter maps coming from the theory of the periodic dressing chain and matrix KdV equation are discussed.