Isomorphism between super Yangian and quantum loop superalgebra. I

TL;DR

This paper establishes an isomorphism between the super Yangian and quantum loop superalgebra associated with the special linear superalgebra, advancing the understanding of their algebraic structures.

Contribution

It constructs an explicit isomorphism between super Yangian and quantum loop superalgebra for A(m,n), extending previous work to superalgebras.

Findings

Confirmed the isomorphism between super Yangian and quantum loop superalgebra

Extended the algebraic framework to superalgebras

Provided explicit construction of the isomorphism

Abstract

Following V. Toledano-Laredo and S. Gautam approach we construct isomorphism between super $\hbar$-Yangian $Y_{\hbar}(A(m,n))$ of special linear superalgebra and quantum loop superalgebra $U_{\hbar}(LA(m,n))$.