Dynamical Yang–Baxter Maps with an Invariance Condition

  • Youichi Shibukawa

    Hokkaido University, Sapporo, Japan


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.

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