alexa Yang–Baxter maps and integrable dynamics


Journal of Generalized Lie Theory and Applications

Author(s): AP Veselov

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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.

This article was published in Physics Letters A and referenced in Journal of Generalized Lie Theory and Applications

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