Dynamical Yang-Baxter maps with an invariance condition

Abstract

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. © 2007 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.