Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions
Abstract
Boundary solutions to the quantum Yang-Baxter (qYB) equation are defined to be those in the boundary of (but not in) the variety of solutions to the ``modified'' qYB equation, the latter being analogous to the modified classical Yang-Baxter (cYB) equation. We construct, for a large class of solutions
r
to the modified cYB equation, explicit ``boundary quantizations'', i.e., boundary solutions to the qYB equation of the form
I+tr+
t
2
r
2
+...
. In the last section we list and give quantizations for all classical r-matrices in
sl(3)∧sl(3)
.