Universal R-matrix of quantum affine gl(1,1)

TL;DR

This paper constructs the universal R-matrix for the quantum affine superalgebra of gl(1,1) by expressing it as a Casimir element derived from a Hopf pairing, utilizing explicit coproduct formulas.

Contribution

It provides an explicit realization of the universal R-matrix for quantum affine gl(1,1) using Hopf pairing and coproduct formulas, advancing understanding of quantum superalgebras.

Findings

Explicit formula for the universal R-matrix as a Casimir element

Realization of the R-matrix via Hopf pairing

Detailed coproduct formulas for Drinfeld loop generators

Abstract

The universal $R$-matrix of the quantum affine superalgebra associated to the Lie superalgebra $\mathfrak{gl}(1,1)$ is realized as the Casimir element of certain Hopf pairing, based on the explicit coproduct formula of all the Drinfeld loop generators.