$RLL$-Realization and Its Hopf Superalgebra Structure of $U_{p, q}(\widehat{\mathfrak{gl}(m|n))}$

TL;DR

This paper extends the Reshetikhin-Semenov-Tian-Shansky formulation to a two-parameter quantum affine superalgebra, deriving its Drinfeld realization and Hopf algebra structure with coproducts for the generators.

Contribution

It introduces a new two-parameter quantum affine superalgebra and provides its Drinfeld realization and Hopf algebra structure, including coproducts.

Findings

Drinfeld realization of $U_{p, q}(\widehat{rak{gl}}(m|n))$ obtained

Hopf algebra structure with Drinfeld-type coproducts established

Extension of quantum affine algebra formulations to superalgebras

Abstract

In this paper, we extend the Reshetikhin-Semenov-Tian-Shansky formulation of quantum affine algebras to the two-parameter quantum affine superalgebra $U_{p, q}(\widehat{\mathfrak{gl}}(m|n))$ and obtain its Drinfeld realization. We also derive its Hopf algebra structure by providing Drinfeld-type coproduct for the Drinfeld generators.