Hopf algebras of dimension 2p^2

TL;DR

This paper classifies non-semisimple Hopf algebras of dimension 2p^2 over an algebraically closed field of characteristic zero, showing that either the algebra or its dual is pointed, thus completing the classification for these dimensions.

Contribution

It proves that for such Hopf algebras, either the algebra or its dual is pointed, advancing the classification of Hopf algebras of dimension 2p^2.

Findings

H or H^* is pointed for non-semisimple Hopf algebras of dimension 2p^2

Completes the classification of these Hopf algebras

Advances understanding of structure in low-dimensional Hopf algebras

Abstract

Let H be a non-semisimple Hopf algebra of dimension 2p^2 over an algebraically closed field of characteristic zero, where p is an odd prime. We prove that H or H^* is pointed, which completes the classification for Hopf algebras of these dimensions.