The r-matrix of the Alday-Arutyunov-Frolov model

Understand

We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation.

• Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form.
• We then employ and make a suitable generalization of the regularization technique proposed by Maillet for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices.
• We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Maillet's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.