On the Gelfand-Kirillov dimension of Pointed Hopf algebras

Details On the Gelfand-Kirillov dimension of Pointed Hopf algebras On the Gelfand-Kirillov dimension of Pointed Hopf algebras

2012-02-19

arxiv.org/abs/1202.4121v1

Mathematics

Rings and Algebras

Scientific paper

Let $H$ be a pointed Hopf algebra. We show that under some mild assumptions $H$ and its associated graded Hopf algebra $\gr H$ have the same Gelfand-Kirillov dimension. As an application, we prove that the Gelfand-Kirillov dimension of a connected Hopf algebra is either infinity or a positive integer. We also classify connected Hopf algebras of GK-dimension three over an algebraically closed field of characteristic zero.

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