Drinfeld realization of the centrally extended $\mathfrak{p}\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }2)$ Yangian algebra with the manifest coproducts

The Lie superalgebra $\mathfrak{p}\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }2)$ 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 $\mathfrak{p}\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }2)$. 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.