Speaker
Description
For affine special superalgebra $\mathfrak{\hat{g}}(\Pi)$ defined by an arbitrary systems of simple roots $\Pi$ we define the affine super Yangian $Y_{\hbar}(\hat{g}(\Pi))$ as Hopf superalgebra which is a quantization of superbialgebra $\hat{g}(\Pi)[t]$ and describe super Yangian in terms of minimalistic system of generators. We consider Drinfeld presentation for $Y^D_{\hbar}(\hat{g}(\Pi))$ and prove that these two presentations are isomorphic as associative superalgebras. We induce by means of this isomorphism a comultiplication on Drinfeld presentation $Y^D_{\hbar}(\hat{g}(\Pi))$ of the super Yangian. We introduce action of Weyl groupoid by isomorphisms on super Yangians as extension of its action on universal enveloping algebra and deformation of action on universal enveloping superalgebra of current Lie superalgebra and prove that such extension is exist and unique. We also discuss the possibility of generalizing the considered constructions to the case of the Yangian of affinization $\hat{\mathfrak{g}}$ of the basic Lie superalgebra $\mathfrak{g}$.
