Abstract
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.
Information
Published: 1 January 2007
First available in Project Euclid: 24 November 2014
zbMATH: 1232.81023
MathSciNet: MR2269130
Digital Object Identifier: 10.2969/msjmemoirs/01701C060
Rights: Copyright © 2007, The Mathematical Society of Japan
