Construction of the Affine Super Yangian

Abstract

In this paper, we define the affine super Yangian $Y\_{\varepsilon\_1,\varepsilon\_2}(\widehat{\mathfrak{sl}}(m|n))$ with a coproduct structure. We also obtain an evaluation homomorphism, that is, an algebra homomorphism from $Y\_{\varepsilon\_1,\varepsilon\_2}(\widehat{\mathfrak{sl}}(m|n))$ to the completion of the universal enveloping algebra of $\widehat{\mathfrak{gl}}(m|n)$.