JournalsprimsVol. 43 , No. 4DOI 10.2977/prims/1201012384

Dynamical Yang–Baxter Maps with an Invariance Condition

  • Youichi Shibukawa

    Hokkaido University, Sapporo, Japan
Dynamical Yang–Baxter Maps with an Invariance Condition cover

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.