Classification of PM Quiver Hopf Algebras

Details Classification of PM Quiver Hopf Algebras Classification of PM Quiver Hopf Algebras

2004-10-06

arxiv.org/abs/math/0410150v15

Journal of Algebra and Its Applications, 6(2007)6, 919-950.

Mathematics

Quantum Algebra

32pages, to appear in Journal of Algebra and its Applications

Scientific paper

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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