On semisimple Hopf algebras of dimension $2q^3$

TL;DR

This paper proves that all semisimple Hopf algebras of dimension 2q^3 over an algebraically closed field of characteristic 0 are semisolvable, meaning they can be constructed from group algebras or their duals through extensions.

Contribution

It establishes a classification result showing such Hopf algebras are always semisolvable, extending understanding of their structure for this specific dimension.

Findings

All semisimple Hopf algebras of dimension 2q^3 are semisolvable.

Such Hopf algebras can be obtained via extensions from group algebras or their duals.

Abstract

Let $q$ be a prime number, $k$ an algebraically closed field of characteristic 0, and $H$ a semisimple Hopf algebra of dimension $2q^3$. This paper proves that $H$ is always semisolvable. That is, such Hopf algebras can be obtained by (a number of) extensions from group algebras or duals of group algebras.