  By means of left quasigroups L=(L, .) and ternary systems, we construct
dynamical Yang-Baxter maps associated with L, L, and (.) satisfying an
invariance condition that the binary operation (.) 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.
