Classical integrable lattice models through quantum group related formalism

TL;DR

This paper develops a formalism connecting quantum group constructions to classical integrable lattice models, enabling the creation of new models and revealing novel structures within existing ones.

Contribution

It introduces a method to derive classical Lax operators and r-matrices from quantum group frameworks using Yang-Baxterisation, expanding the class of integrable models.

Findings

Generated new types of collective integrable lattice models

Constructed classical Lax operators and r-matrices from quantum algebra

Revealed nonstandard r-matrices in canonical models

Abstract

We translate effectively our earlier quantum constructions to the classical language and using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan algebra are able to construct Lax operators and associated $r$-matrices of classical integrable models. Thus new as well as known lattice systems of different classes are generated including new types of collective integrable models and canonical models with nonstandard $r$ matrices.