Dynamical Yang-Baxter Maps with an Invariance Condition
Quantum Algebra
2007-05-23 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0704.3109,
title = {Dynamical Yang-Baxter Maps with an Invariance Condition},
author = {Youichi Shibukawa},
journal= {arXiv preprint arXiv:0704.3109},
year = {2007}
}