Yang-Baxter maps: dynamical point of view

Details Yang-Baxter maps: dynamical point of view Yang-Baxter maps: dynamical point of view

2006-12-28

arxiv.org/abs/math/0612814v1

Mathematics

Quantum Algebra

24 pages. Extended version of lectures given at the meeting "Combinatorial Aspect of Integrable Systems" (RIMS, Kyoto, July 20

Scientific paper

A review of some recent results on the dynamical theory of the Yang-Baxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics. The relations with matrix factorisations, matrix KdV solitons, Poisson Lie groups, geometric crystals and tropical combinatorics are discussed and demonstrated on several concrete examples.

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