English

Some Hopf Algebras related to $\mathfrak{sl}_2$

Quantum Algebra 2021-01-25 v2

Abstract

We define a series of Artin-Schelter Gorenstein Hopf algebras HβH_\beta with injective dimensions 3. Radford's Hopf algebra and Gelaki's Hopf algebra are homomorphic images of HβH_\beta. We determine its Grothendieck ring G0(Hβ)G_0(H_\beta). Meanwhile we can obtain Grothendieck rings of Gelaki's Hopf algebras and Radford's Hopf algebras U(N,ν,ω)U_{(N,\nu,\omega)} in \cite{R}, and non-isomorphic Hopf algebras with isomorphic Grothendieck rings.

Keywords

Cite

@article{arxiv.1901.04163,
  title  = {Some Hopf Algebras related to $\mathfrak{sl}_2$},
  author = {Yan Tan and Jing Wang and Zhixiang Wu},
  journal= {arXiv preprint arXiv:1901.04163},
  year   = {2021}
}