English

Coproducts for affine super-Yangian and Weyl groupoid action

Quantum Algebra 2025-10-07 v1

Abstract

For affine special linear superalgebra sl^(mn,Π)\widehat{sl}(m|n, \Pi) defined by an arbitrary system of simple roots Π\Pi we define the affine super Yangian Y(sl^(mn,Π))Y_{\hbar}(\widehat{sl}(m|n, \Pi)) as Hopf superalgebra which is a quantization of superbialgebra sl^(mn,Π)[t]\widehat{sl}(m|n, \Pi)[t] and describe super Yangian in terms of minimalistic system of generators. We consider Drinfeld presentation for YD(sl^(mn,Π))Y^D_{\hbar}(\widehat{sl}(m|n, \Pi)) 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 YD(sl^(mn,Π))Y^D_{\hbar}(\widehat{sl}(m|n, \Pi)) 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 Y(sl^(mn,Π1))Y_{\hbar}(\widehat{sl}(m|n, \Pi_1)) and Y(sl^(mn,Π2))Y_{\hbar}(\widehat{sl}(m|n, \Pi_2)), defined by different simple root systems Π1 \Pi_1 and Π2 \Pi_2 are isomorphic as Hopf superalgebras.

Keywords

Cite

@article{arxiv.2510.04221,
  title  = {Coproducts for affine super-Yangian and Weyl groupoid action},
  author = {Vasiliy Volkov and Vladimir Stukopin},
  journal= {arXiv preprint arXiv:2510.04221},
  year   = {2025}
}