Drinfeld Isomorphism for Novel Quantum Affine Algebra of Type $A_{1}^{(1)}$

TL;DR

This paper establishes an algebraic isomorphism between a newly defined quantum affine algebra of type A1^(1) and its Drinfeld realization, enhancing understanding of its structure through explicit construction and proof.

Contribution

It constructs the Drinfeld realization of the novel quantum affine algebra and proves their algebraic isomorphism, providing a new perspective on its structure.

Findings

Established the Drinfeld isomorphism for the novel quantum affine algebra

Constructed mma-invariant generating functions for the algebra

Proved algebraic equivalence between the original and Drinfeld realizations

Abstract

In this paper, we first review the definition of the novel quantum affine algebra \(U_{\textbf{q}}(\widehat{\mathfrak{sl}}_2)\) of type \(A_{1}^{(1)}\) given in \cite{FHZ, HZhuang}. Furthermore, by introducing \(\Omega\)-invariant generating functions, we construct the Drinfeld realization \(U^{D}_{\textbf{q}}(\widehat{\mathfrak{sl}}_2)\) of this algebra, and prove that \(U_{\textbf{q}}(\widehat{\mathfrak{sl}}_2)\) and \(U^{D}_{\textbf{q}}(\widehat{\mathfrak{sl}}_2)\) are algebraically isomorphic, which is known as the Drinfeld Isomorphism.