1203.1063 (Alexei Kitaev et al.)

Solutions to generalized Yang-Baxter equations via ribbon fusion
categories    [PDF]

Alexei Kitaev, Zhenghan Wang

Inspired by quantum information theory, we look for representations of the braid groups $B_n$ on $V^{\otimes (n+m-2)}$ for some fixed vector space $V$ such that each braid generator $\sigma_i, i=1,...,n-1$ acts on $m$ consecutive tensor factors from $i$ through $i+m-1$. The $m=2$ case corresponds to the Yang-Baxter equation. We observe that certain simple objects in ribbon fusion categories naturally give rise to such representations for the case $m=3$. Examples are given from the theories $SO(N)_2$. The representation from the Jones-Kauffman theory at a $6^{th}$ root of unity, which is closely related to $SO(3)_2$ or $SU(2)_4$, is explicitly described in the end.

View original: http://arxiv.org/abs/1203.1063