Yang-Baxter maps and integrable dynamics
量子代数
2009-11-07 v2 动力系统
摘要
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.
引用
@article{arxiv.math/0205335,
title = {Yang-Baxter maps and integrable dynamics},
author = {A. P. Veselov},
journal= {arXiv preprint arXiv:math/0205335},
year = {2009}
}
备注
Revised version based on the talks at NEEDS conference (Cadiz, 10-15 June 2002) and SIDE-V conference (Giens, 21-26 June 2002)