Dynamical Yang-Baxter maps

Abstract

We propose and investigate dynamical Yang-Baxter maps, some of which produce solutions to the quantum dynamical Yang-Baxter equation. Suppose that L is a loop and a group. If their unit elements coincide, then L gives birth to a bijective dynamical Yang-Baxter map from L × L to L × L whose dynamical parameter belongs to L. The above group L is abelian if and only if the corresponding dynamical Yang-Baxter map satisfies the unitary condition.