Structure theorems for semisimple Hopf algebras of dimension $pq^3$

TL;DR

This paper establishes structure theorems for semisimple Hopf algebras of dimension pq^3, where p and q are primes with p > q^3, over an algebraically closed field of characteristic zero.

Contribution

It provides the first comprehensive structure theorems for semisimple Hopf algebras of this specific dimension, expanding understanding of their classification.

Findings

Structure theorems for semisimple Hopf algebras of dimension pq^3

Classification results under the condition p > q^3

Advances in the theory of Hopf algebra structures

Abstract

Let $p,q$ be prime numbers with $p>q^3$, and $k$ an algebraically closed field of characteristic 0. In this paper, we obtain the structure theorems for semisimple Hopf algebras of dimension $pq^3$.