1203.2037 (Theodoros E. Kouloukas et al.)

3D compatible ternary systems and Yang-Baxter maps    [PDF]

Theodoros E. Kouloukas, Vassilios G. Papageorgiou

According to Shibukawa, ternary systems defined on quasigroups and satisfying certain conditions provide a way of constructing dynamical Yang-Baxter maps with invariant condition and vice versa. After noticing that these conditions can be interpreted as 3-dimensional compatibility of equations on quad-graphs we investigate when the associated dynamical Yang-Baxter maps are in fact Yang-Baxter maps. In some cases these maps can be obtained as reductions of higher dimensional maps through compatible constraints.

View original: http://arxiv.org/abs/1203.2037