3D compatible ternary systems and Yang-Baxter maps

Details 3D compatible ternary systems and Yang-Baxter maps 3D compatible ternary systems and Yang-Baxter maps

2012-03-09

arxiv.org/abs/1203.2037v1

Physics

Mathematical Physics

11 pages

Scientific paper

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.

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