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Classification of PM Quiver Hopf Algebras

Shouchuan Zhang·Yao-Zhong Zhang·Hui-Xiang Chen
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Abstract

We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field $k$ is the complex field and $G$ is a finite abelian group, we classify quiver Hopf algebras over $G$, multiple Taft algebras over $G$ and Nichols algebras in $^{kG}_{kG} {\cal YD}$. We show that the quantum enveloping algebra of a complex semisimple Lie algebra is a quotient of a semi-path Hopf algebra.

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Shouchuan Zhang, Yao-Zhong Zhang, Hui-Xiang Chen. 2004-10-06. Classification of PM Quiver Hopf Algebras. https://arxiv.org/abs/math/0410150

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