Classification of pointed Hopf algebras of dimension $p^2$ over any algebraically closed field

Abstract

Let $p$ be a prime. We complete the classification on pointed Hopf algebras of dimension $p^2$ over an algebraically closed field $k$. When $\text{char}k\ne p$, our result is the same as the well-known result for $\text{char}k=0$. When $\text{char}k=p$, we obtain 14 types of pointed Hopf algebras of dimension $p^2$, including a unique noncommutative and noncocommutative type.

10 pages, no figures

References in corpus (3)

• Connected Hopf Algebras of Dimension $p^2$
• Classification of pointed rank one Hopf algebras
• On Hopf algebras of dimension 4p

Cited by in corpus (5)

• Classification of connected Hopf algebras of dimension $p^3$ I
• Local criteria for cocommutative Hopf algebras
• Computing indicators of Radford algebras
• On non-connected pointed Hopf algebras of dimension 16 in characteristic 2
• Pointed Hopf algebras of dimension $p^{2}q$ in characteristic $p$