Classification of PM Quiver Hopf Algebras

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 ${}_{kG}^{kG}\mathcal{YD}$. We show that the quantum enveloping algebra of a complex semisimple Lie algebra is a quotient of a semi-path Hopf algebra.

arXiv comment32pages, to appear in Journal of Algebra and its Applications

References in corpus (1)

• Homological Dimension of Crossed Products