2025/10/05 by Volkov, Vasiliy, Stukopin, Vladimir
#FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2510.04221
For affine special linear superalgebra \widehatsl(m|n, Π) defined by an arbitrary system of simple roots Π we define the affine super Yangian Yℏ(\widehatsl(m|n, Π)) as Hopf superalgebra which is a quantization of superbialgebra \widehatsl(m|n, Π)[t] and describe super Yangian in terms of minimalistic system of generators. We consider Drinfeld presentation for YDℏ(\widehatsl(m|n, Π)) and prove that these two presentations are isomorphic as associative superalgebras. We induce by means of this isomorphism a co-multiplication on the Drinfeld presentation YDℏ(\widehatsl(m|n, Π)) of the super Yangian. We introduce the action of Weyl groupoid by isomorphisms on super Yangians as an extension of its action on universal enveloping algebra and deformation of action on univesal enveloping superalgebra of current Lie superalgebra and prove that such extension exists and unique. As a consequence of this construction we obtain that super Yangians Yℏ(\widehatsl(m|n, Π1)) and Yℏ(\widehatsl(m|n, Π2)), defined by different simple root systems Π1 and Π2 are isomorphic as Hopf superalgebras.