Drinfeld realization of the centrally extended $\mathfrak{psl}(2|2)$ Yangian algebra with the manifest coproducts

TL;DR

This paper constructs the Drinfeld realization of the Yangian algebra for the centrally extended superalgebra rak{psl}(2|2), demonstrating its Hopf algebra structure with explicit coproducts, advancing understanding of its algebraic properties.

Contribution

It provides the first explicit Drinfeld realization of the Yangian for rak{psl}(2|2) with manifest coproducts, including a proof of their existence and isomorphism to Levendorskii's realization.

Findings

Established the Drinfeld realization with manifest coproducts.

Proved the isomorphism between Levendorskii's realization and the Drinfeld realization.

Confirmed the Hopf algebra structure of the Yangian.

Abstract

The Lie superalgebra $\mathfrak{psl}(2|2)$ is recognized as a pretty special one in both mathematics and theoretical physics. In this paper, we present the Drinfeld realization of the Yangian algebra associated with the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$. Furthermore, we show that it possesses the Hopf algebra structures, particularly the coproducts. The idea to prove the existence of the manifest coproducts is the following. Firstly, we shall introduce them to Levendorskii's realization, a system of a finite truncation of the Drinfeld generators. Secondly, we show that Levendorskii's realization is isomorphic to the Drinfeld realization by induction.