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.