Yang-Baxter maps and integrable dynamics

Details Yang-Baxter maps and integrable dynamics Yang-Baxter maps and integrable dynamics

2002-05-31

arxiv.org/abs/math/0205335v2

Mathematics

Quantum Algebra

Revised version based on the talks at NEEDS conference (Cadiz, 10-15 June 2002) and SIDE-V conference (Giens, 21-26 June 2002)

Scientific paper

10.1016/S0375-9601(03)00915-0

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.

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