The quantum bialgebra associated with the eight-vertex R-matrix

TL;DR

This paper introduces a quantum bialgebra derived from Baxter's eight-vertex R-matrix, representing a deformation of the Lie algebra of automorphic functions on a complex torus, expanding the algebraic structures in quantum integrable systems.

Contribution

It constructs a new quantum bialgebra associated with the eight-vertex R-matrix as a deformation of a classical Lie algebra, linking quantum groups with automorphic functions.

Findings

Defined the quantum bialgebra structure

Connected the algebra to automorphic functions on a complex torus

Extended the framework of quantum deformations in integrable models

Abstract

The quantum bialgebra related to the Baxter's eight-vertex R-matrix is found as a quantum deformation of the Lie algebra of sl(2)-valued automorphic functions on a complex torus.