On quantum Freidel-Maillet algebra for non-ultralocal integrable systems

TL;DR

This paper develops a quantum algebra framework for non-ultralocal integrable systems, using Sklyanin's product to regularize singular operator products, aligning with classical Maillet symmetrization.

Contribution

It introduces a regularization method for quantum transition matrix algebra in non-ultralocal systems, connecting quantum and classical formulations.

Findings

Regularized quantum algebra reproduces Maillet's classical symmetrization

Sklyanin's product ensures well-defined quantum operator expressions

Framework bridges quantum and classical integrable system descriptions

Abstract

We consider the quantum algebra of transition matrices for non-ultralocal integrable systems, and show that a regularization of the singular operator products in the quantum algebra via Sklyanin's product leads to well-defined expressions, reproducing in the classical limit Maillet's symmetrization prescription for Poisson brackets.