Set-theoretical reflection equation: Classification of reflection maps

Caudrelier, V., Crampe, N. & Zhang, Q. C. (2013). Set-theoretical reflection equation: Classification of reflection maps. Journal of Physics A: Mathematical and Theoretical, 46(095203), doi: 10.1088/1751-8113/46/9/095203

Abstract

The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context of quadrirational Yang-Baxter maps. We provide a method for constructing reflection maps and we obtain a classification of solutions associated to all the families of quadrirational Yang-Baxter maps that have been classified recently.