Dynamical Yang–Baxter Maps with an Invariance Condition

Abstract

By means of left quasigroups $L=(L,\cdot )$ and ternary systems, we construct dynamical Yang–Baxter maps associated with $L$, $L$, and $(\cdot )$ satisfying an invariance condition that the binary operation $(\cdot )$ of the left quasigroup $L$ defines. Conversely, this construction characterize such dynamical Yang–Baxter maps. The unitary condition of the dynamical Yang–Baxter map is discussed. Moreover, we establish a correspondence between two dynamical Yang–Baxter maps constructed in this paper. This correspondence produces a version of the vertex-IRF correspondence.