2007/04/24 by Youichi Shibukawa, Shibukawa, Youichi
Mathematics · #20F36 #20N05 #20N10 (Secondary) #81R50 (Primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.0704.3109
openalex publication_date 2007/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.