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arXiv · 1901.04163

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

Yan Tan·Jing Wang·Zhixiang Wu
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Abstract

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

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Yan Tan, Jing Wang, Zhixiang Wu. 2021-01-22. Some Hopf Algebras related to $\mathfrak{sl}_2$. https://arxiv.org/abs/1901.04163

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