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

Abstract

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.

39 pages; misprints corrected, references added

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Cited by in corpus (4)

• On the quantization of continuous non-ultralocal integrable systems
• On the equivalence theorem for integrable systems
• Integrable theories and generalized graded Maillet algebras
• The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator