Dynamical Yang-Baxter Maps with an Invariance Condition

Details Dynamical Yang-Baxter Maps with an Invariance Condition Dynamical Yang-Baxter Maps with an Invariance Condition

2007-04-24

arxiv.org/abs/0704.3109v1

Mathematics

Quantum Algebra

27 pages

Scientific paper

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.

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