DYNAMICAL YANG-BAXTER MAPS

Abstract. In this work, we propose and investigate dynamical Yang-Baxter maps, some of which produce solutions to the quantum dynam-ical 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 be-longs to L. The above group L is abelian if and only if the corresponding dynamical Yang-Baxter map satisfies the unitary condition. 1