Dynamical Yang–Baxter Maps with an Invariance Condition

  • Youichi Shibukawa

    Hokkaido University, Sapporo, Japan

Abstract

By means of left quasigroups and ternary systems, we construct dynamical Yang–Baxter maps associated with , , and satisfying an invariance condition that the binary operation of the left quasigroup 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.

Cite this article

Youichi Shibukawa, Dynamical Yang–Baxter Maps with an Invariance Condition. Publ. Res. Inst. Math. Sci. 43 (2007), no. 4, pp. 1157–1182

DOI 10.2977/PRIMS/1201012384